Let A and B be two 3 × 3 real matrices such that A 2 - B 2 is invertible matrix. If A 5 = B 5 and A 3 B 2 = A 2 B 3 , then the value of the determinant of the matrix A 3 + B 3 is equal to :

Step-by-step solution

Let C = A 2 - B 2 ; C ≠ 0 and A 5 = B 5       . . . 1 A 3   B 2 = A 2   B 3       . . . 2 Subtracting equation 2 from 1 , we get A 5 - A 3 B 2 = B 5 - A 2 B 3 ⇒ A 3   A 2 - B 2 + B 3   A 2 - B 2 = O Post multiplying inverse of A 2 - B 2 : A 3 + B 3 = O ⇒ A 3 + B 3 = 0