If and x2 = –1, then show that (A + B)2 = A2 + B2.

As, LHS = (A + B)2 =


⇒ LHS =


By matrix multiplication we can write LHS as –


LHS =


⇒ LHS =


Given x2 = -1


∴ LHS =


RHS = A2 + B2 =


⇒ RHS =


By matrix multiplication we can write-


RHS =


Given x2 = -1


∴ RHS =


Clearly RHS = LHS =


Hence, (A + B)2 = A2 + B2 …proved


34