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Question
Mathematics
If the matrices A=[ai j] and B=[bi j] are of same order, say m × n, satisfy the commutative law, then
Q. If the matrices
A
=
[
a
ij
]
and
B
=
[
b
ij
]
are of same order, say
m
×
n
, satisfy the commutative law, then
184
172
Matrices
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A
A
+
B
=
B
−
A
B
A
+
B
=
B
+
A
C
A
+
B
=
A
−
B
D
None of these
Solution:
Commutative law If
A
=
[
a
ij
]
,
B
=
[
b
ij
]
are matrices of the same order, say
m
×
n
, then
A
+
B
=
B
+
A
.
Now,
A
+
B
=
[
a
ij
]
+
[
b
ij
]
=
[
a
ij
+
b
ij
]
=
[
b
ij
+
a
ij
]
(
∵
addition of numbers is commutative
)
=
(
[
b
ij
]
+
[
a
ij
]
)
=
B
+
A