EduSahara™ Assignment
Name : Matrix Multiplication
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If A =
[
5
7
4
3
]
and B =
[
7
7
6
-9
]
, then A
✕
B =
(i)
[
77
-28
46
3
]
(ii)
[
77
-28
47
1
]
(iii)
[
77
-31
46
1
]
(iv)
[
77
-28
45
1
]
(v)
[
77
-28
46
1
]
Question
2
2.
Which of the following is an identity matrix ?
(i)
[
3
0
0
1
]
(ii)
[
1
0
0
2
]
(iii)
[
1
-3
0
1
]
(iv)
[
1
-1
0
1
]
(v)
[
1
0
0
1
]
Question
3
3.
If A =
[
0
-2
1
1
2
3
3
-1
1
]
and B =
[
3
1
-1
-1
2
-2
-2
2
-2
]
, then A
✕
B =
(i)
[
0
-2
2
-5
11
-11
5
3
-3
]
(ii)
[
0
-2
2
-5
11
-11
8
2
-3
]
(iii)
[
0
-2
4
-5
11
-11
8
3
-3
]
(iv)
[
0
-1
2
-5
11
-11
8
3
-3
]
(v)
[
0
-2
2
-5
11
-11
8
3
-3
]
Question
4
4.
If A =
[
-2
-1
2
-1
0
-2
]
and B =
[
2
-2
3
1
2
-2
]
, then A
✕
B =
(i)
[
-3
-1
-6
6
]
(ii)
[
-3
-1
-9
6
]
(iii)
[
-3
-1
-4
6
]
(iv)
[
-2
-2
8
-7
-3
4
-2
-2
8
]
(v)
[
-2
-7
-2
-2
-3
-2
8
4
8
]
Question
5
5.
If A =
[
4
2
3
-1
-4
3
0
3
-3
]
, then
A
2
=
(i)
[
14
9
11
0
23
-24
-3
-21
18
]
(ii)
[
14
9
9
0
22
-24
-3
-21
18
]
(iii)
[
14
9
9
0
23
-24
-3
-21
18
]
(iv)
[
14
9
9
1
23
-24
-3
-21
18
]
(v)
[
14
9
9
0
23
-24
-6
-21
18
]
Question
6
6.
If A =
[
-3
4
2
1
-3
2
-2
2
0
]
, then
6
A =
(i)
[
-18
24
12
6
-18
12
-12
12
0
]
(ii)
[
-18
24
12
6
-18
12
-13
12
0
]
(iii)
[
-17
24
12
6
-18
12
-12
12
0
]
(iv)
[
-18
24
12
6
-18
12
-12
10
0
]
(v)
[
-18
24
14
6
-18
12
-12
12
0
]
Question
7
7.
If A =
[
-1
2
-2
-2
]
, B =
[
-1
2
-2
1
]
and C =
[
2
0
1
2
]
,
then (A
✕
B)
✕
C =
(i)
[
-6
0
6
-12
]
(ii)
[
-6
1
6
-12
]
(iii)
[
-8
0
6
-12
]
(iv)
[
-4
0
6
-12
]
(v)
[
-7
0
6
-12
]
Question
8
8.
If A =
[
0
2
1
2
]
, B =
[
1
1
-1
-1
]
and C =
[
2
1
-1
-1
]
,
then (A
✕
B)
+
C =
(i)
[
0
-3
-2
-2
]
(ii)
[
0
-1
-2
-1
]
(iii)
[
-1
-1
-2
-2
]
(iv)
[
0
-1
-2
-2
]
(v)
[
0
2
-2
-2
]
Question
9
9.
If A =
[
1
0
-1
1
]
, B =
[
-1
2
2
-1
]
and C =
[
2
0
1
1
]
,
then A
✕
(B
+
C ) =
(i)
[
4
2
2
-2
]
(ii)
[
1
2
1
-2
]
(iii)
[
1
2
2
-1
]
(iv)
[
1
2
2
-2
]
(v)
[
-1
2
2
-2
]
Question
10
10.
If A =
[
-4
3
-5
-1
]
and C =
[
-51
-2
41
-21
-12
37
]
,
find a matrix B satisfying A
✕
B = C
(i)
[
6
2
-8
-9
5
3
]
(ii)
[
6
2
-8
-9
0
3
]
(iii)
[
6
2
-8
-10
2
3
]
(iv)
[
6
2
-8
-9
2
3
]
(v)
[
6
2
-7
-9
2
3
]
Question
11
11.
If A =
[
0
2
0
-2
]
, B =
[
0
-2
-2
-1
-2
1
]
and C =
[
2
0
-2
1
-2
-2
-2
-1
0
]
,
then compute the product (A
✕
B)
✕
C =
(i)
[
-12
8
12
12
-6
-12
]
(ii)
[
-12
6
12
12
-6
-12
]
(iii)
[
-11
6
12
12
-6
-12
]
(iv)
[
-12
6
10
12
-6
-12
]
(v)
[
-13
6
12
12
-6
-12
]
Question
12
12.
If A =
[
-2
3
1
-8
]
, B =
[
-6
-4
8
-7
]
and C =
[
-2
1
7
3
]
,
then compute
A
2
+
BC =
(i)
[
-10
-48
-75
54
]
(ii)
[
-9
-48
-75
54
]
(iii)
[
-9
-48
-74
54
]
(iv)
[
-9
-48
-75
51
]
(v)
[
-9
-48
-73
54
]
Question
13
13.
If A =
[
-1
3
0
1
]
, then find AI
(i)
[
-1
4
0
1
]
(ii)
[
-1
2
0
1
]
(iii)
[
-1
3
-3
1
]
(iv)
[
-1
3
0
1
]
(v)
[
2
3
0
1
]
Question
14
14.
If A =
[
-3
-2
-7
-4
]
, then find B satisfying A
✕ B = A
(i)
[
1
-1
0
1
]
(ii)
[
1
0
0
1
]
(iii)
[
1
1
0
1
]
(iv)
[
-1
0
0
1
]
(v)
[
1
0
3
1
]
Question
15
15.
Which of the following are true for matrices A, B and C ?
a)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
b)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
c)
(
A
✕
I
)
=
(
I
✕
A
)
= I
d)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
e)
(
A
✕
I
)
=
(
I
✕
A
)
= A
f)
(
A
✕
B
)
=
(
B
✕
A
)
(i)
{a,b,e}
(ii)
{c,a}
(iii)
{d,a,b}
(iv)
{f,c,e}
(v)
{d,b}
Question
16
16.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
,
then the order of
(
A
✕
B
)
is
(i)
m ✕ o
(ii)
o ✕ m
(iii)
n ✕ o
(iv)
m ✕ n
Question
17
17.
If A =
[
4
4
4
9
]
and B =
[
1
9
1
5
]
, find
(
A
+
B
)
(
A
−
B
)
(i)
[
54
27
57
34
]
(ii)
[
54
27
55
31
]
(iii)
[
54
27
57
31
]
(iv)
[
53
27
57
31
]
(v)
[
55
27
57
31
]
Question
18
18.
If A =
[
4
2
6
2
]
and B =
[
8
6
1
2
]
, find
A
2
−
B
2
(i)
[
-42
-48
23
6
]
(ii)
[
-42
-48
26
9
]
(iii)
[
-42
-48
26
7
]
(iv)
[
-42
-48
26
6
]
(v)
[
-42
-48
26
5
]
Question
19
19.
If A =
[
7
7
4
2
]
and B =
[
8
8
9
9
]
, find
(
A
+
B
)
2
(i)
[
421
390
338
316
]
(ii)
[
420
390
336
316
]
(iii)
[
420
390
340
316
]
(iv)
[
419
390
338
316
]
(v)
[
420
390
338
316
]
Question
20
20.
If A =
[
1
1
8
1
]
and B =
[
2
2
3
6
]
, find
A
2
+
B
2
+
2AB
(i)
[
26
34
78
95
]
(ii)
[
30
34
78
95
]
(iii)
[
29
34
78
94
]
(iv)
[
29
34
81
95
]
(v)
[
29
34
78
95
]
Question
21
21.
If A =
[
4
2
3
7
]
and B =
[
8
9
1
9
]
, find
(
A
−
B
)
2
(i)
[
2
42
-12
-8
]
(ii)
[
2
42
-11
-10
]
(iii)
[
2
41
-12
-10
]
(iv)
[
0
42
-12
-10
]
(v)
[
2
42
-12
-10
]
Question
22
22.
If A =
[
4
7
5
8
]
and B =
[
4
7
8
8
]
, find
A
2
+
B
2
−
2AB
(i)
[
-21
3
-12
21
]
(ii)
[
-21
0
-12
21
]
(iii)
[
-20
0
-12
21
]
(iv)
[
-23
0
-12
21
]
(v)
[
-21
0
-13
21
]
Question
23
23.
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 cols 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 rows in B
d)
If A X B is possible, the no of rows in A must be equal to no of cols in B
(i)
{a,c}
(ii)
{d,a,c}
(iii)
{c}
(iv)
{b,c}
Question
24
24.
If A =
[
(
−
1
)
(
−
7
)
]
, B =
[
x
y
]
, then
(
A
✕
B
)
=
(i)
[
(
−
x
)
(
−
y
)
(
−
7
x
)
(
−
7
y
)
]
(ii)
[
(
−
x
−
7
y
)
(
−
x
−
7
y
)
]
(iii)
[
(
−
x
−
7
y
)
(
−
x
−
7
y
)
]
(iv)
[
(
−
x
)
(
−
7
x
)
(
−
y
)
(
−
7
y
)
]
(v)
[
(
−
x
−
7
y
)
]
Question
25
25.
If A =
[
2
-9
6
8
]
and B =
[
2
-2
-7
2
]
and D =
[
-76
32
82
-20
]
,
4
A
−
6
B
+
8
C
= D, then C = ?
(i)
[
-9
9
2
-5
]
(ii)
[
-9
7
2
-5
]
(iii)
[
-9
8
2
-5
]
(iv)
[
-9
7
0
-5
]
(v)
[
-10
7
2
-5
]
Question
26
26.
If A =
[
a
b
c
d
]
, B =
[
-6
2
4
2
]
and C =
[
-38
16
32
6
]
and
(
A
✕
B
)
= C , find A
(i)
[
7
0
-2
5
]
(ii)
[
7
1
-2
5
]
(iii)
[
7
3
-2
5
]
(iv)
[
7
1
-2
2
]
(v)
[
7
1
-2
6
]
Question
27
27.
If B =
[
5
5
7
6
]
and C =
[
86
78
17
16
]
and
(
A
✕
B
)
= C , find A
(i)
[
6
7
2
1
]
(ii)
[
9
8
2
1
]
(iii)
[
6
8
-1
1
]
(iv)
[
6
8
2
1
]
(v)
[
6
8
3
1
]
Question
28
28.
If B =
[
7
1
5
1
]
and C =
[
67
11
]
and
(
A
✕
B
)
= C , find A
(i)
[
6
8
]
(ii)
[
5
5
]
(iii)
[
6
6
]
(iv)
[
6
5
]
(v)
[
4
5
]
Question
29
29.
Given A =
[
1
-6
-6
-5
]
find B such that AB = BA = A
(i)
[
1
2
0
1
]
(ii)
[
1
0
0
0
]
(iii)
[
1
1
0
1
]
(iv)
[
1
-2
0
1
]
(v)
[
1
0
0
1
]
Question
30
30.
Find X if A =
[
1
4
8
-1
]
, AX = B and B =
[
21
-10
36
52
]
(i)
[
5
6
5
-4
]
(ii)
[
5
6
4
-2
]
(iii)
[
5
6
3
-4
]
(iv)
[
3
6
4
-4
]
(v)
[
5
6
4
-4
]
Question
31
31.
Given A =
[
7
-1
9
3
]
and B =
[
47
99
]
,
find P such that AP = B
(i)
[
8
6
]
(ii)
[
8
9
]
(iii)
[
7
9
]
(iv)
[
11
9
]
(v)
[
8
10
]
Question
32
32.
Given A =
[
-1
3
-2
-2
-2
0
-3
-3
3
]
and B =
[
4
0
-6
]
,
find P such that AP = B
(i)
[
1
0
-2
]
(ii)
[
0
0
-3
]
(iii)
[
0
0
-2
]
(iv)
[
0
0
1
]
(v)
[
0
-3
-2
]
Assignment Key
1) (v)
2) (v)
3) (v)
4) (i)
5) (iii)
6) (i)
7) (i)
8) (iv)
9) (iv)
10) (iv)
11) (ii)
12) (ii)
13) (iv)
14) (ii)
15) (i)
16) (i)
17) (iii)
18) (iv)
19) (v)
20) (v)
21) (v)
22) (ii)
23) (iii)
24) (v)
25) (ii)
26) (ii)
27) (iv)
28) (iv)
29) (v)
30) (v)
31) (ii)
32) (iii)
