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

Options

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

Answer

B

Explanation

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