Let A be a nonsingular matrix Show thatSolutionFor any nonsi

Solution

For any nonsingular matrices A and B of nxn order , we can say that

det(A) * det(B) = det(AB)

Let A = A^-1 and B = A

=> det(A^-1) * det(A) = det(A^-1A)

=> det(A^-1) * det(A) = det(I)

=> det(A^-1) * det(A) = 1

=> det(A^-1) = 1/det(A)