Let AB and C be 5 by 5 matrices whose determinants are 234 r

Let A,B, and C be 5 by 5 matrices whose determinants are 2,3,4 respectively. Find:

det(-A)

det(AB)

det(C^-1)

Solution

here A is an 5×5 square matrix where 5 is odd, then

det(-A) = det(A) = 2

det(AB) = det(A)*det(B) = 2*3 = 6

det(C^-1) = det(C)^-1 = (4)^-1 = 1/4