MatricesHard

Question

If A and B are square matrices of size n × n such that A2 − B2 = (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 an identity matrix

Solution

A2 - B2 = (A - B) (A + B)
A2 - B2 = A2 + AB - BA - B2
⇒ AB = BA.

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