Question

Let A be a square matrix of order 3 such that det.(A) = 1/2 , then det.(adj.A^–1) is equal to 

(A) 16 

(B) 8 

(C) 4 

(D) 2

Answer 1

Correct Answer is: (C) 4 

We know that |adj. A| = |A|^n–1 , where n is oder of square matrix A.

For n = 3 ; |adj. A^–1| = |A–¹|² = 1/|A|² = 1/(1/)² = 4.