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Byju's Answer
Standard XII
Mathematics
Inverse of a Matrix
Multiplicatio...
Question
Multiplication of two matrices is not commutative, but the value of trace of AB will be equal to trace of BA.
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Solution
[
a
b
c
d
]
[
e
f
g
h
]
[
a
e
+
b
g
a
f
+
b
h
c
e
+
d
g
e
f
+
h
d
]
T
r
a
c
e
(
A
B
)
=
a
e
+
b
g
+
c
f
+
h
d
[
e
f
g
h
]
[
a
b
c
d
]
[
e
a
+
c
f
e
b
+
d
f
a
g
+
c
h
g
b
+
h
d
]
T
r
a
c
e
(
B
A
)
=
e
a
+
c
f
+
h
b
+
h
d
=
e
a
+
b
g
+
c
f
+
h
d
=
T
r
a
c
e
(
A
B
)
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1
Similar questions
Q.
Let
A
and
B
are two square matrices such that the trace of
A
B
=
30
,
then the trace of
B
A
is equal to
Q.
Let
A
and
B
be two symmetric matrices of order 3.
Statement-1:
A
(
B
A
)
and
(
A
B
)
A
are symmetric matrices.
Statement-2:
A
B
is symmetric matrix if matrix multiplication of
A
and
B
is commutative.
Q.
Let A and B be two symmetic matrices of order 3.
Statement - 1 :
A
(
B
A
)
and
(
A
B
)
A
are symmetric matrices.
Statement - 2 :
A
B
is symmetric matrix if matrix multiplication of
A
and
B
is commutative.
Q.
If the trace of
A
B
is
30
then the trace of
B
A
is
Q.
Let two matrices
A
and
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of order
2
×
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m
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n
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and
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n
respectively. If the matrix multiplication
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exist. Then the value of
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