Which of the following is true?

(A) For any orthogonal matrix A, we haveA′A = ILet B be a matrix such that AB = I.Now we haveA′ = A′ I                [by property of unit matrix]= A′(AB) = (A′A)B = IB = BTherefore, (A′)′(A) = AA′ = AB = I⇒ A′ is orthogonal.(B) For any orthogonal matrix A, we haveA′A = I⇒ |A′A| = |I| ⇒ |A′| |A| = 1⇒ |A| ≠ 0, i.e., A is non-singular.(C) Let A and B be two orthogonal matrices, therefore,(AB)′ (AB) = B′A′AB             [by property of transpose]= B′(A′A)B                           [by associative law]= B′(IB) = B′B = I⇒ AB is orthogonal.(D) Let A be orthogonal matrix and B be its inverse matrix.Then, we have,A′A = I                                                 (1)and, AB = I = BA                                 (2)Now, we have,(AB)′ (AB) = B′A′AB= B′(A′A)B = B′(IB)B = B′B                    (3)Also, from equation (2), we have(AB)′ = I′ = Ii.e., B′B = I                                             [Using equation (3)]⇒ B is orthogonal.The correct option is (A), (B), (C) and (D)