# Determinant - Linear Algebra

• Oct 23rd 2007, 04:39 PM
pakman
Determinant - Linear Algebra
Let A be a nonsingular matrix. Show that

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

I know that for a nxn matrix det(A^T) = det(A)... don't see how this one goes though... thanks in advance.
• Oct 23rd 2007, 04:46 PM
ThePerfectHacker
$\det (AA^{-1}) = \det I = 1$
Thus,
$\det(A) \det(A^{-1}) = 1$