# linear algebra help

• Mar 23rd 2009, 08:28 AM
lord12
linear algebra help
Show if A is invertible that A^-1 = 1/detA. I'm sort of stuck on this.
• Mar 23rd 2009, 08:34 AM
TheEmptySet
Quote:

Originally Posted by lord12
Show if A is invertible that A^-1 = 1/detA. I'm sort of stuck on this.

We know that $\det(AB)=\det(A)\det(B)$

using this and the property that $AA^{-1}=I$ we get

$\det(AA^{-1})=\det(I)$

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