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Byju's Answer
Standard XII
Mathematics
Transpose of a Matrix
Let A and B b...
Question
Let A and B be square matrices of the order 3 × 3. Is (AB)
2
= A
2
B
2
? Give reasons.
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Solution
Yes, (AB)
2
= A
2
B
2
if AB = BA.
If AB = BA, then
(AB)
2
= (AB)(AB)
= A(BA)B (associative law)
= A(AB)B
= A
2
B
2
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