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  1. #1
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    linear algebra help

    Show if A is invertible that A^-1 = 1/detA. I'm sort of stuck on this.
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  2. #2
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    Quote Originally Posted by lord12 View Post
    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})}
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