Let A = 1 2 3 4 and B = p q r s are two matrices such that A B = B A and r ≠ 0 , then the value of 3 p - 3 s 5 q - 4 r is equal to

Step-by-step solution

A B = 1 2 3 4 p q r s = p + 2 r q + 2 s 3 p + 4 r 3 q + 4 s B A = p q r s 1 2 3 4 = p + 3 q 2 p + 4 q r + 3 s 2 r + 4 s ∵ A B = B A ⇒ p + 2 r = p + 3 q ⇒ 2 r = 3 q ⇒ q + 2 s = 2 p + 4 q ⇒ 2 s = 2 p + 3 q ⇒ 3 p + 4 r = r + 3 s ⇒ p + r = s ⇒ p - s = - r ⇒ 3 q + 4 s = 2 r + 4 s ⇒ 2 r = 3 q 3 p - s 5 q - 4 r = 3 - r 5 2 r 3 - 4 r = - 3 10 3 - 4 = 9 2 = 4.5