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 :

Question

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 :, 2, 4, 1, 0

MARKS App · Accepted Answer

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

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