Let A be a diagonalizable matrix whose eigenvalues are all either 1 or -1. Show that [tex]A^{-1}=A[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A=X\begin{bmatrix}

\pm 1 & \cdots & 0 \\

\vdots & \ddots & \vdots \\

0 & \cdots & \pm 1

\end{bmatrix}X^{-1}

[/tex] and [tex]A^{-1}=X\begin{bmatrix}

\pm 1 & \cdots & 0 \\

\vdots & \ddots & \vdots \\

0 & \cdots & \pm 1

\end{bmatrix}^{-1}X^{-1}

[/tex]

How do I show they are equal?

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# Homework Help: Diagonalizable matrix A^-1=a

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