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

If A and 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

`AB=BA`

B

Either of A or B is a zero matrix

C

Either of A or B is na identity matrix

D

`A=B`

Text Solution

Verified by Experts

The correct Answer is:
A
Since `A^(2)-B^(2)=(A-B)(A+B)=A^(2)+B^(2)+AB-BA`
So `AB-BA=OimpliesAB=BA`
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