Let A B be 3 Times 3 matrices with detA 3 and detB 2 Find

Let A, B be 3 Times 3 matrices with det(A) = 3 and det(B) = 2. Find the determinant of A^2 (2B) (3A)^-1. 8/9 16/9 4 8/3 None of the above.

Solution

det(A²)=(detA)² =(3)² = 9

3A means each row of A is multiplied by 3 and this is a 3x3 matrix so determinant will be multiplied by 3³

det((3A)^-1) = [det(3A)]^-1=[3³det(A)]^-1=1/(27*3)=1/81

det(2B)=2³det(B)=16

hence det (A²(2B)(3A)^-1)= 9*(1/81)*16=16/9=1.7777