EduSahara™ Assignment
Name : Matrix Multiplication Concepts
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The order of matrix A =
[
-1
-1
]
is
(i)
1 ✕ 2
(ii)
2 ✕ 2
(iii)
1 ✕ 1
(iv)
3 ✕ 1
(v)
2 ✕ 1
Question
2
2.
The order of matrix A =
[
1
4
]
is
(i)
2 ✕ 3
(ii)
2 ✕ 1
(iii)
1 ✕ 2
(iv)
1 ✕ 3
(v)
2 ✕ 2
Question
3
3.
The order of matrix A =
[
-4
-2
-2
]
is
(i)
2 ✕ 4
(ii)
3 ✕ 1
(iii)
1 ✕ 4
(iv)
1 ✕ 3
(v)
2 ✕ 3
Question
4
4.
The order of matrix A =
[
5
-5
-3
-1
]
is
(i)
2 ✕ 1
(ii)
2 ✕ 2
(iii)
2 ✕ 3
(iv)
1 ✕ 2
(v)
3 ✕ 2
Question
5
5.
If the elements of matrix A are multiplied with -1 , we get
(i)
additive inverse of A
(ii)
additive identity of A
(iii)
multiplicative inverse of A
(iv)
multiplicative identity of A
Question
6
6.
If the elements of matrix A are multiplied with 0 , we get
(i)
multiplicative inverse of A
(ii)
additive inverse of A
(iii)
multiplicative identity of A
(iv)
additive identity of A
Question
7
7.
A
4 ✕ 2
matrix has
a)
2
rows and
4
columns
b)
6
rows and
2
columns
c)
4
rows and
2
columns
d)
4
rows and
8
columns
(i)
{d,a,c}
(ii)
{c}
(iii)
{a,c}
(iv)
{b,c}
Question
8
8.
Which of the following are true for matrices A and B ?
a)
The orders of
(
A
✕
B
)
and
(
B
✕
A
)
are same
b)
If A and B can be multiplied, they must have the same order
c)
If A and B can be added, they must have the same order
d)
If AB = 0, A = 0 or B = 0 or both A and B are zero matrices
(i)
{c}
(ii)
{a,c}
(iii)
{b,c}
(iv)
{d,a,c}
Question
9
9.
Which of the following are true ?
a)
The order of
(
A
✕
B
)
and
(
B
✕
A
)
is same
b)
If AB = 0, then A = 0 or B = 0 or both A & B are 0
c)
If matrices A & B can be multiplied, they must have the same order
d)
If matrices A & B can be added, they must have the same order
(i)
{c,a,d}
(ii)
{b,d}
(iii)
{a,d}
(iv)
{d}
Question
10
10.
Which of the following are true for matrices A, B and C ?
a)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
b)
(
A
✕
B
)
=
(
B
✕
A
)
c)
(
A
✕
I
)
=
(
I
✕
A
)
= I
d)
(
A
✕
I
)
=
(
I
✕
A
)
= A
e)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
f)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
(i)
{c,a,f}
(ii)
{b,d,e}
(iii)
{d,e,f}
(iv)
{b,e}
(v)
{a,d}
Question
11
11.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
,
then the order of
(
A
✕
B
)
is
(i)
m ✕ n
(ii)
m ✕ o
(iii)
o ✕ m
(iv)
n ✕ o
Question
12
12.
Which of the following are true ?
a)
If A X B is possible, the no of rows in A must be equal to no of rows in B
b)
If A X B is possible, the no of rows in A must be equal to no of cols in B
c)
If A X B is possible, the no of cols in A must be equal to no of cols in B
d)
If A X B is possible, the no of cols in A must be equal to no of rows in B
(i)
{a,d}
(ii)
{b,d}
(iii)
{d}
(iv)
{c,a,d}
Question
13
13.
If A =
[
a
b
c
d
]
and B =
[
p
q
r
s
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
b
r
a
q
+
b
s
c
p
+
d
r
c
q
+
d
s
]
(ii)
[
a
p
+
b
q
a
r
+
b
s
c
p
+
d
q
c
r
+
d
s
]
(iii)
[
p
a
+
q
c
p
b
+
q
d
r
a
+
s
c
r
b
+
s
d
]
(iv)
[
a
p
+
b
r
c
p
+
d
r
a
q
+
b
s
c
q
+
d
s
]
(v)
[
a
p
+
c
q
a
r
+
c
s
b
p
+
d
q
b
r
+
d
s
]
Question
14
14.
If A =
[
a
b
c
d
e
f
]
and B =
[
p
q
r
s
t
u
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
b
r
+
c
t
d
p
+
e
r
+
f
t
a
q
+
b
s
+
c
u
d
q
+
e
s
+
f
u
]
(ii)
[
a
p
+
d
q
a
r
+
d
s
a
t
+
d
u
b
p
+
e
q
b
r
+
e
s
b
t
+
e
u
c
p
+
f
q
c
r
+
f
s
c
t
+
f
u
]
(iii)
[
a
b
c
d
e
f
]
(iv)
[
a
p
+
b
r
+
c
t
a
q
+
b
s
+
c
u
d
p
+
e
r
+
f
t
d
q
+
e
s
+
f
u
]
(v)
[
p
a
+
q
d
p
b
+
q
e
p
c
+
q
f
r
a
+
s
d
r
b
+
s
e
r
c
+
s
f
t
a
+
u
d
t
b
+
u
e
t
c
+
u
f
]
Question
15
15.
If A =
[
a
b
c
d
e
f
g
h
i
]
and B =
[
p
q
r
s
t
u
v
w
x
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
b
s
+
c
v
a
q
+
b
t
+
c
w
a
r
+
b
u
+
c
x
d
p
+
e
s
+
f
v
d
q
+
e
t
+
f
w
d
r
+
e
u
+
f
x
g
p
+
h
s
+
i
v
g
q
+
h
t
+
i
w
g
r
+
h
u
+
i
x
]
(ii)
[
a
p
+
b
s
+
c
v
d
p
+
e
s
+
f
v
g
p
+
h
s
+
i
v
a
q
+
b
t
+
c
w
d
q
+
e
t
+
f
w
g
q
+
h
t
+
i
w
a
r
+
b
u
+
c
x
d
r
+
e
u
+
f
x
g
r
+
h
u
+
i
x
]
(iii)
[
a
p
+
b
q
+
c
r
a
s
+
b
t
+
c
u
a
v
+
b
w
+
c
x
d
p
+
e
q
+
f
r
d
s
+
e
t
+
f
u
d
v
+
e
w
+
f
x
g
p
+
h
q
+
i
r
g
s
+
h
t
+
i
u
g
v
+
h
w
+
i
x
]
(iv)
[
a
p
+
d
q
+
g
r
a
s
+
d
t
+
g
u
a
v
+
d
w
+
g
x
b
p
+
e
q
+
h
r
b
s
+
e
t
+
h
u
b
v
+
e
w
+
h
x
c
p
+
f
q
+
i
r
c
s
+
f
t
+
i
u
c
v
+
f
w
+
i
x
]
(v)
[
p
a
+
q
d
+
r
g
p
b
+
q
e
+
r
h
p
c
+
q
f
+
r
i
s
a
+
t
d
+
u
g
s
b
+
t
e
+
u
h
s
c
+
t
f
+
u
i
v
a
+
w
d
+
x
g
v
b
+
w
e
+
x
h
v
c
+
w
f
+
x
i
]
Question
16
16.
If A =
[
a
11
a
12
a
21
a
22
]
and B =
[
b
11
b
12
b
21
b
22
]
,
then
(
A
✕
B
)
=
(i)
[
a
11
b
11
+
a
12
b
12
a
11
b
21
+
a
12
b
22
a
21
b
11
+
a
22
b
12
a
21
b
21
+
a
22
b
22
]
(ii)
[
a
11
b
11
+
a
21
b
12
a
11
b
21
+
a
21
b
22
a
12
b
11
+
a
22
b
12
a
12
b
21
+
a
22
b
22
]
(iii)
[
b
11
a
11
+
b
12
a
21
b
11
a
12
+
b
12
a
22
b
21
a
11
+
b
22
a
21
b
21
a
12
+
b
22
a
22
]
(iv)
[
a
11
b
11
+
a
12
b
21
a
21
b
11
+
a
22
b
21
a
11
b
12
+
a
12
b
22
a
21
b
12
+
a
22
b
22
]
(v)
[
a
11
b
11
+
a
12
b
21
a
11
b
12
+
a
12
b
22
a
21
b
11
+
a
22
b
21
a
21
b
12
+
a
22
b
22
]
Question
17
17.
If A =
[
a
11
a
12
a
13
a
21
a
22
a
23
]
and B =
[
b
11
b
12
b
21
b
22
b
31
b
32
]
,
then
(
A
✕
B
)
=
(i)
[
a
11
b
11
+
a
12
b
21
+
a
13
b
31
a
21
b
11
+
a
22
b
21
+
a
23
b
31
a
11
b
12
+
a
12
b
22
+
a
13
b
32
a
21
b
12
+
a
22
b
22
+
a
23
b
32
]
(ii)
[
a
11
a
12
a
13
a
21
a
22
a
23
]
(iii)
[
a
11
b
11
+
a
12
b
21
+
a
13
b
31
a
11
b
12
+
a
12
b
22
+
a
13
b
32
a
21
b
11
+
a
22
b
21
+
a
23
b
31
a
21
b
12
+
a
22
b
22
+
a
23
b
32
]
(iv)
[
a
11
b
11
+
a
21
b
12
a
11
b
21
+
a
21
b
22
a
11
b
31
+
a
21
b
32
a
12
b
11
+
a
22
b
12
a
12
b
21
+
a
22
b
22
a
12
b
31
+
a
22
b
32
a
13
b
11
+
a
23
b
12
a
13
b
21
+
a
23
b
22
a
13
b
31
+
a
23
b
32
]
(v)
[
b
11
a
11
+
b
12
a
21
b
11
a
12
+
b
12
a
22
b
11
a
13
+
b
12
a
23
b
21
a
11
+
b
22
a
21
b
21
a
12
+
b
22
a
22
b
21
a
13
+
b
22
a
23
b
31
a
11
+
b
32
a
21
b
31
a
12
+
b
32
a
22
b
31
a
13
+
b
32
a
23
]
Question
18
18.
If A =
[
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
]
and B =
[
b
11
b
12
b
13
b
21
b
22
b
23
b
31
b
32
b
33
]
,
then
(
A
✕
B
)
=
(i)
[
b
11
a
11
+
b
12
a
21
+
b
13
a
31
b
11
a
12
+
b
12
a
22
+
b
13
a
32
b
11
a
13
+
b
12
a
23
+
b
13
a
33
b
21
a
11
+
b
22
a
21
+
b
23
a
31
b
21
a
12
+
b
22
a
22
+
b
23
a
32
b
21
a
13
+
b
22
a
23
+
b
23
a
33
b
31
a
11
+
b
32
a
21
+
b
33
a
31
b
31
a
12
+
b
32
a
22
+
b
33
a
32
b
31
a
13
+
b
32
a
23
+
b
33
a
33
]
(ii)
[
a
11
b
11
+
a
12
b
12
+
a
13
b
13
a
11
b
21
+
a
12
b
22
+
a
13
b
23
a
11
b
31
+
a
12
b
32
+
a
13
b
33
a
21
b
11
+
a
22
b
12
+
a
23
b
13
a
21
b
21
+
a
22
b
22
+
a
23
b
23
a
21
b
31
+
a
22
b
32
+
a
23
b
33
a
31
b
11
+
a
32
b
12
+
a
33
b
13
a
31
b
21
+
a
32
b
22
+
a
33
b
23
a
31
b
31
+
a
32
b
32
+
a
33
b
33
]
(iii)
[
a
11
b
11
+
a
12
b
21
+
a
13
b
31
a
11
b
12
+
a
12
b
22
+
a
13
b
32
a
11
b
13
+
a
12
b
23
+
a
13
b
33
a
21
b
11
+
a
22
b
21
+
a
23
b
31
a
21
b
12
+
a
22
b
22
+
a
23
b
32
a
21
b
13
+
a
22
b
23
+
a
23
b
33
a
31
b
11
+
a
32
b
21
+
a
33
b
31
a
31
b
12
+
a
32
b
22
+
a
33
b
32
a
31
b
13
+
a
32
b
23
+
a
33
b
33
]
(iv)
[
a
11
b
11
+
a
21
b
12
+
a
31
b
13
a
11
b
21
+
a
21
b
22
+
a
31
b
23
a
11
b
31
+
a
21
b
32
+
a
31
b
33
a
12
b
11
+
a
22
b
12
+
a
32
b
13
a
12
b
21
+
a
22
b
22
+
a
32
b
23
a
12
b
31
+
a
22
b
32
+
a
32
b
33
a
13
b
11
+
a
23
b
12
+
a
33
b
13
a
13
b
21
+
a
23
b
22
+
a
33
b
23
a
13
b
31
+
a
23
b
32
+
a
33
b
33
]
(v)
[
a
11
b
11
+
a
12
b
21
+
a
13
b
31
a
21
b
11
+
a
22
b
21
+
a
23
b
31
a
31
b
11
+
a
32
b
21
+
a
33
b
31
a
11
b
12
+
a
12
b
22
+
a
13
b
32
a
21
b
12
+
a
22
b
22
+
a
23
b
32
a
31
b
12
+
a
32
b
22
+
a
33
b
32
a
11
b
13
+
a
12
b
23
+
a
13
b
33
a
21
b
13
+
a
22
b
23
+
a
23
b
33
a
31
b
13
+
a
32
b
23
+
a
33
b
33
]
Question
19
19.
If A =
[
(
−
9
)
3
]
, B =
[
x
y
]
, then
(
A
✕
B
)
=
(i)
[
(
−
9
x
+
3
y
)
(
−
9
x
+
3
y
)
]
(ii)
[
(
−
9
x
)
(
−
9
y
)
3
x
3
y
]
(iii)
[
(
−
9
x
+
3
y
)
(
−
9
x
+
3
y
)
]
(iv)
[
(
−
9
x
)
3
x
(
−
9
y
)
3
y
]
(v)
[
(
−
9
x
+
3
y
)
]
Question
20
20.
Find
[
x
y
]
[
a
b
c
d
]
[
x
y
]
(i)
[
x
2
a
+
y
b
x
+
x
c
y
+
y
2
d
]
(ii)
[
x
2
a
+
x
y
c
x
2
b
+
x
y
d
y
x
a
+
y
2
c
y
x
b
+
y
2
d
]
(iii)
[
x
2
+
y
2
]
(iv)
[
x
a
y
+
y
2
b
+
x
2
c
+
y
d
x
]
(v)
[
x
2
a
+
y
c
x
+
x
b
y
+
y
2
d
]
Question
21
21.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
and C is
o ✕ p
,
then the order of
(
A
✕
B
)
✕
C
is
(i)
m ✕ o
(ii)
n ✕ p
(iii)
m ✕ p
(iv)
o ✕ m
(v)
p ✕ m
Question
22
22.
If the order of matrix
(
A
✕
B
)
is
4 ✕ 1
and the order of B =
3 ✕ 1
,
then the order of A is ?
(i)
4 ✕ 2
(ii)
5 ✕ 4
(iii)
4 ✕ 3
(iv)
5 ✕ 3
(v)
4 ✕ 4
Question
23
23.
If the order of matrix
(
A
✕
B
)
is
1 ✕ 5
and the order of A =
1 ✕ 5
,
then the order of B is ?
(i)
5 ✕ 5
(ii)
6 ✕ 6
(iii)
6 ✕ 5
(iv)
5 ✕ 6
(v)
4 ✕ 5
Question
24
24.
If A =
[
7
3
-4
5
]
and the sum of the values of
elements of matrix kA =
99
, find k
(i)
9
(ii)
7
(iii)
11
(iv)
10
(v)
8
Question
25
25.
Find the
multiplicative
identity of matrix A =
[
2
-4
-9
3
]
(i)
[
1
0
1
1
]
(ii)
[
1
0
2
1
]
(iii)
[
1
-1
0
1
]
(iv)
[
1
0
0
1
]
(v)
[
1
-2
0
1
]
Question
26
26.
Find the
multiplicative
identity of matrix A =
[
2
-2
4
4
-4
-2
3
-3
1
]
(i)
[
1
0
0
3
1
0
0
0
1
]
(ii)
[
1
0
0
0
1
0
0
0
1
]
(iii)
[
1
0
0
-3
1
0
0
0
1
]
(iv)
[
1
0
0
1
1
0
0
0
1
]
(v)
[
1
0
0
0
1
0
0
0
0
]
Question
27
27.
Which of the following pairs of matrices can be multiplied?
(i)
[
4
9
0
8
]
,
[
-4
5
-6
9
9
-5
]
(ii)
[
-3
5
-1
]
,
[
-4
5
-6
9
9
-5
]
(iii)
[
4
9
0
8
]
,
[
-6
-2
]
(iv)
[
-3
0
-6
]
,
[
0
7
-4
-8
7
5
]
(v)
[
4
9
0
8
]
,
[
-2
7
3
4
]
Question
28
28.
Which of the following pairs of matrices can be multiplied?
(i)
[
-6
-3
1
-2
-7
-3
]
,
[
-5
4
-4
-3
5
9
]
(ii)
[
7
-8
-7
-3
]
,
[
-8
6
]
(iii)
[
-2
5
4
]
,
[
-6
-3
1
-2
-7
-3
]
(iv)
[
7
-8
-7
-3
]
,
[
-6
-3
1
-2
-7
-3
]
(v)
[
6
8
-6
]
,
[
-5
4
-4
-3
5
9
]
Question
29
29.
Which of the following pairs of matrices can be multiplied?
(i)
[
-7
-5
-9
]
,
[
-6
3
-8
4
-9
-6
]
(ii)
[
3
7
8
]
,
[
0
3
6
3
9
1
]
(iii)
[
9
5
-5
-8
]
,
[
-6
3
-8
4
-9
-6
]
(iv)
[
9
5
-5
-8
]
,
[
-1
7
]
(v)
[
-1
7
]
,
[
7
-1
]
Question
30
30.
Which of the following pairs of matrices can be multiplied?
(i)
[
3
6
3
5
]
,
[
-1
-6
4
0
5
1
]
(ii)
[
3
6
3
5
]
,
[
-9
-8
]
(iii)
[
6
0
1
]
,
[
6
9
-2
]
(iv)
[
6
9
-2
]
,
[
6
-7
6
2
2
2
]
(v)
[
6
0
1
]
,
[
-1
-6
4
0
5
1
]
Question
31
31.
Which of the following pairs of matrices can be multiplied?
(i)
[
-7
-5
9
5
3
-2
]
,
[
4
-7
6
]
(ii)
[
1
2
-5
-9
]
,
[
-3
3
]
(iii)
[
-5
8
5
]
,
[
-7
-5
9
5
3
-2
]
(iv)
[
4
-7
6
]
,
[
-1
2
4
9
-7
-4
]
(v)
[
1
2
-5
-9
]
,
[
-1
2
4
9
-7
-4
]
Question
32
32.
Which of the following pairs of matrices can be multiplied?
(i)
[
0
-4
-3
4
]
,
[
4
0
]
(ii)
[
0
-2
-4
]
,
[
-8
9
-8
2
6
-6
]
(iii)
[
-4
0
-9
]
,
[
-3
2
8
-4
-3
-2
]
(iv)
[
4
0
]
,
[
-3
2
8
-4
-3
-2
]
(v)
[
0
-4
-3
4
]
,
[
-8
9
-8
2
6
-6
]
Question
33
33.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
1 ✕ 2 , 2 ✕ 1
(ii)
1 ✕ 2 , 2 ✕ 3
(iii)
1 ✕ 3 , 2 ✕ 3
(iv)
3 ✕ 1 , 1 ✕ 3
(v)
2 ✕ 3 , 3 ✕ 1
Question
34
34.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
3 ✕ 1 , 1 ✕ 3
(ii)
2 ✕ 3 , 3 ✕ 1
(iii)
1 ✕ 2 , 2 ✕ 3
(iv)
1 ✕ 2 , 2 ✕ 1
(v)
3 ✕ 2 , 1 ✕ 2
Question
35
35.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
1 ✕ 2 , 2 ✕ 1
(ii)
3 ✕ 1 , 1 ✕ 3
(iii)
2 ✕ 2 , 3 ✕ 3
(iv)
1 ✕ 2 , 2 ✕ 3
(v)
2 ✕ 3 , 3 ✕ 1
Question
36
36.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
3 ✕ 1 , 3 ✕ 2
(ii)
2 ✕ 3 , 3 ✕ 1
(iii)
1 ✕ 2 , 2 ✕ 3
(iv)
1 ✕ 2 , 2 ✕ 1
(v)
3 ✕ 1 , 1 ✕ 3
Question
37
37.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
1 ✕ 2 , 2 ✕ 3
(ii)
3 ✕ 1 , 3 ✕ 2
(iii)
3 ✕ 1 , 1 ✕ 3
(iv)
1 ✕ 2 , 2 ✕ 1
(v)
2 ✕ 3 , 3 ✕ 1
Question
38
38.
Express the following equation in the matrix form
a
1
x
+
b
1
y
+
c
1
= 0 and
a
2
x
+
b
2
y
+
c
2
= 0
(i)
[
a
1
b
1
a
2
b
2
]
[
c
1
c
2
]
+
[
x
y
]
= 0
(ii)
[
a
1
b
1
a
2
b
2
]
[
x
y
]
[
c
1
c
2
]
= 0
(iii)
[
a
1
a
2
b
1
b
2
]
[
x
y
]
+
[
c
1
c
2
]
= 0
(iv)
[
a
1
b
1
a
2
b
2
]
[
x
y
]
+
[
c
1
c
2
]
= 0
Assignment Key
1) (v)
2) (iii)
3) (iv)
4) (ii)
5) (i)
6) (iv)
7) (ii)
8) (i)
9) (iv)
10) (iii)
11) (ii)
12) (iii)
13) (i)
14) (iv)
15) (i)
16) (v)
17) (iii)
18) (iii)
19) (v)
20) (v)
21) (iii)
22) (iii)
23) (i)
24) (i)
25) (iv)
26) (ii)
27) (v)
28) (i)
29) (v)
30) (iii)
31) (i)
32) (iv)
33) (iii)
34) (v)
35) (iii)
36) (i)
37) (ii)
38) (iv)
