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.

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- Oct 23rd 2007, 04:39 PMpakmanDeterminant - 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 PMThePerfectHacker
$\displaystyle \det (AA^{-1}) = \det I = 1$

Thus,

$\displaystyle \det(A) \det(A^{-1}) = 1$