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