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If A and B f are square matrices of size...

If A and B f are square matrices of size `nxxn` such that
`A^(2) - B^(2) = (A - B) (A+ B)` which of the following will be
always true?

A

A = B

B

AB =BA

C

either A or B is a zero matrix

D

either A or B is an identity matrix

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`A^2-B^2=(A-B)(A+B)`
`rArr A^2-B^2=A(A-B)-B(A+B)`
`rArr A^2-B^2=A^2+AB-BA-B^2`
`rArr AB=BA`
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