Question

sa se calculeze determinantul matricei A la puterea 2010

A=$\left[\begin{array}{ccc}-1&0\\3&-1\end{array}\right]$

Answer 1

$A^{2} = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] = I_{2}$
$A^{3}= A^{2} x A= \left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right] =A$
$A^{4}= A^{3} x A= \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]= I_{2}$
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$A^{2010} = (A^{2})^{1005}= ( I_{2} )^{1005}= I_{2}$