Verify that A^2 = I, when A= 0&1&-1 4&-3&4 3&-3&4 . - Vidyadip

Question

Verify that $A^2 = I$, when $\text{A}=\begin{bmatrix}0&1&-1\\4&-3&4\\3&-3&4\end{bmatrix}.$

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Answer

We have, $\text{A}=\begin{bmatrix}0&1&-1\\4&-3&4\\3&-3&4\end{bmatrix}$
$\therefore\ \text{A}^2=\begin{bmatrix}0&1&-1\\4&-3&4\\3&-3&4\end{bmatrix}.\begin{bmatrix}0&1&-1\\4&-3&4\\3&-3&4\end{bmatrix}$ $[\because\ \text{A}^2=\text{A}.\text{A}]$$=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}=\text{I}$
Hence proved.

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