EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If A =
[
3
1
2
-1
]
, then find AI
(i)
[
4
1
2
-1
]
(ii)
[
2
1
2
-1
]
(iii)
[
3
1
2
-1
]
(iv)
[
3
1
2
1
]
(v)
[
3
1
-1
-1
]
Question
2
2.
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 ✕ 1
(iv)
3 ✕ 1 , 3 ✕ 2
(v)
1 ✕ 2 , 2 ✕ 3
Question
3
3.
Find the transpose of matrix A =
[
3
7
0
4
]
(i)
[
3
0
7
2
]
(ii)
[
4
0
7
4
]
(iii)
[
3
2
7
4
]
(iv)
[
3
0
7
4
]
(v)
[
2
0
7
4
]
Question
4
4.
If A =
[
-3
3
-8
-2
]
and C =
[
-15
-50
]
,
find a matrix B satisfying A
✕
B = C
(i)
[
6
0
]
(ii)
[
9
1
]
(iii)
[
6
2
]
(iv)
[
6
-2
]
(v)
[
6
1
]
Question
5
5.
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
21
+
b
21
a
22
+
b
22
]
(ii)
[
a
11
+
b
11
a
21
+
b
12
a
12
+
b
21
a
22
+
b
22
]
(iii)
[
a
11
+
b
11
a
21
+
b
21
a
12
+
b
12
a
22
+
b
22
]
(iv)
[
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
6
6.
If A =
[
2
3
7
4
]
and B =
[
9
4
4
5
]
, find
A
2
+
B
2
−
2AB
(i)
[
62
28
-63
-18
]
(ii)
[
63
28
-60
-18
]
(iii)
[
62
28
-61
-18
]
(iv)
[
62
28
-60
-18
]
(v)
[
62
28
-58
-18
]
Question
7
7.
Which of the following is a square matrix?
(i)
[
7
5
9
2
8
4
9
8
5
8
1
6
]
(ii)
[
5
5
6
5
7
6
]
(iii)
[
1
6
7
7
2
3
7
6
6
6
9
4
2
6
7
1
5
5
3
3
]
(iv)
[
1
7
1
2
1
5
6
7
8
1
1
8
]
(v)
[
7
6
9
5
6
2
6
8
6
]
Question
8
8.
The order of matrix A =
[
1
1
3
-1
2
-2
]
is
(i)
2 ✕ 3
(ii)
2 ✕ 2
(iii)
3 ✕ 3
(iv)
4 ✕ 2
(v)
3 ✕ 2
Question
9
9.
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)
1 ✕ 2 , 2 ✕ 3
(iv)
3 ✕ 2 , 1 ✕ 2
(v)
2 ✕ 3 , 3 ✕ 1
Question
10
10.
If A =
[
9
2
3
6
]
and B =
[
4
2
9
1
]
, find
(
A
+
B
)
2
(i)
[
218
80
240
97
]
(ii)
[
217
82
240
97
]
(iii)
[
215
80
240
97
]
(iv)
[
217
79
240
97
]
(v)
[
217
80
240
97
]
Question
11
11.
If A =
[
1
1
-1
0
2
-1
]
and B =
[
0
-1
1
0
-2
-2
]
, then A
✕
B =
(i)
[
0
-2
1
1
1
-1
-2
-6
4
]
(ii)
[
0
1
-2
-2
1
-6
1
-1
4
]
(iii)
[
1
1
4
2
]
(iv)
[
5
1
4
2
]
(v)
[
3
1
4
2
]
Question
12
12.
If A =
[
3
-4
-4
2
2
1
-4
4
4
]
and B =
[
-1
3
1
-3
-2
2
-4
-2
1
]
, then A
+
B =
(i)
[
0
-1
-3
-1
0
3
-8
2
5
]
(ii)
[
2
-1
-3
-1
-1
3
-8
2
5
]
(iii)
[
2
-1
-3
-1
0
3
-8
2
7
]
(iv)
[
2
-1
-3
-1
0
3
-8
2
5
]
(v)
[
2
-1
-3
0
0
3
-8
2
5
]
Question
13
13.
Which of the following is a null matrix ?
(i)
[
0
0
0
0
]
(ii)
[
0
1
0
0
]
(iii)
[
0
2
0
0
]
(iv)
[
0
0
-2
0
]
(v)
[
0
0
-1
0
]
Question
14
14.
If A =
[
1
1
1
0
]
, B =
[
2
-1
-2
1
]
and C =
[
0
1
-1
-1
]
,
then (A
+
B)
+
C =
(i)
[
0
1
-2
0
]
(ii)
[
3
1
-2
-1
]
(iii)
[
3
1
-2
2
]
(iv)
[
3
1
-2
0
]
(v)
[
3
2
-2
0
]
Question
15
15.
Find the
multiplicative
identity of matrix A =
[
-4
-7
-7
-4
]
(i)
[
1
0
-1
1
]
(ii)
[
1
0
-2
1
]
(iii)
[
1
0
0
1
]
(iv)
[
1
0
1
1
]
(v)
[
1
0
0
4
]
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
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
]
(ii)
[
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
]
(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
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
]
(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
21
a
22
]
and B =
[
b
11
b
12
b
21
b
22
]
,
then
(
A
−
B
)
=
(i)
[
a
11
−
b
11
a
21
−
b
21
a
12
−
b
12
a
22
−
b
22
]
(ii)
[
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
]
(iii)
[
a
11
−
b
11
a
21
−
b
12
a
12
−
b
21
a
22
−
b
22
]
(iv)
[
a
11
−
b
11
a
12
−
b
12
a
21
−
b
21
a
22
−
b
22
]
Question
18
18.
If A =
[
2
1
2
-2
]
, B =
[
1
-1
1
1
]
and C =
[
2
-1
2
1
]
,
then A
✕
(B
+
C ) =
(i)
[
9
-2
-2
-8
]
(ii)
[
9
-2
0
-6
]
(iii)
[
10
-2
0
-8
]
(iv)
[
9
-2
0
-9
]
(v)
[
9
-2
0
-8
]
Question
19
19.
Which of the following are true for matrices A, B and C ?
a)
(
A
✕
B
)
=
(
B
✕
A
)
b)
(
A
✕
I
)
=
(
I
✕
A
)
= A
c)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
d)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
e)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
f)
(
A
✕
I
)
=
(
I
✕
A
)
= I
(i)
{b,c,e}
(ii)
{d,b,c}
(iii)
{f,a,e}
(iv)
{d,c}
(v)
{a,b}
Question
20
20.
Find the
multiplicative
identity of matrix A =
[
4
-4
4
2
0
-2
1
3
-1
]
(i)
[
1
0
0
0
1
0
0
0
-1
]
(ii)
[
1
0
0
0
1
0
0
0
1
]
(iii)
[
1
0
0
0
3
0
0
0
1
]
(iv)
[
1
-1
0
0
1
0
0
0
1
]
(v)
[
1
0
0
0
1
0
1
0
1
]
Question
21
21.
Which of the following are true?
a)
If a matrix is symmetric, then it is a square matrix
b)
If a matrix is symmetric then it is equal to its transpose
c)
A matrix is symmetric if the principal diagonal elements are same
d)
A rectangular matrix cannot be symmetric
(i)
{c,a,b}
(ii)
{c,a}
(iii)
{c,d}
(iv)
{c,b}
(v)
{a,b,d}
Question
22
22.
If A =
[
-9
-4
6
7
]
and B =
[
-1
7
2
-4
]
, then A
+
B =
(i)
[
-10
3
8
3
]
(ii)
[
-10
3
8
1
]
(iii)
[
-10
3
8
4
]
(iv)
[
-7
3
8
3
]
(v)
[
-11
3
8
3
]
Question
23
23.
If A =
[
1
-7
1
7
]
, then find B satisfying A
✕ B = A
(i)
[
1
-3
0
1
]
(ii)
[
1
0
0
2
]
(iii)
[
1
0
0
1
]
(iv)
[
1
0
0
4
]
(v)
[
1
0
-1
1
]
Question
24
24.
If A =
[
1
0
-2
-1
]
, B =
[
0
0
-2
0
]
and C =
[
0
-1
1
1
]
,
then (A
✕
B)
✕
C =
(i)
[
0
0
1
-2
]
(ii)
[
0
0
0
-3
]
(iii)
[
0
0
3
-2
]
(iv)
[
0
0
-2
-2
]
(v)
[
0
0
0
-2
]
Question
25
25.
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
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
]
(ii)
[
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
]
(iii)
[
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
]
(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)
[
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
]
Assignment Key
1) (iii)
2) (iv)
3) (iv)
4) (v)
5) (i)
6) (iv)
7) (v)
8) (v)
9) (iv)
10) (v)
11) (v)
12) (iv)
13) (i)
14) (iv)
15) (iii)
16) (v)
17) (iv)
18) (v)
19) (i)
20) (ii)
21) (v)
22) (i)
23) (iii)
24) (v)
25) (ii)
