If A+B are square matrices of size nxxn...

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

A

A = B

B

AB = BA

C

Either of A or B is a zero matrix

D

Either of A or B is dientity matrix

Verified by Experts

The correct Answer is:

B

`A^(2) - B^(2) =(A-B)(A+B)`
`rArr A^(2) -B^(2) = A^(2) + AB - BA - B^(2)`
`rArr AB = BA`

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