Let A and B are two non-singular matrices of order 3 such that A = 3 and A - 1 B 2 + 2 A B = O , then the value of A 4 - 2 A 2 B is equal to (where O is the null matrix of order 3 )

Step-by-step solution

A - 1 B 2 + 2 A B = O ⇒ A - 1 B B B - 1 + 2 A B B - 1 = O ⇒ A - 1 B + 2 A = O ⇒ A A - 1 B + 2 A A = O ⇒ B = - 2 A 2 Hence, A 4 - 2 A 2 B = 5 A 4 = 5 3 A 4 = 5 3 . 3 4