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  4. If A = [3&7 1&2], then the value of the determinant |A2013 - 3A2012| is equal to

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Q. If $A = \begin{bmatrix}3&7\\ 1&2\end{bmatrix}$, then the value of the determinant $|A^{2013} - 3A^{2012}|$ is equal to

Determinants

Solution:

$| A^{2013} - 3A^{2012} | = | A^{2012} | | A - 3I | = | A |^{2012} | A - 3I|$
$= \left(1\right)\begin{vmatrix}0&7\\ 1&-1\end{vmatrix} = \left(1\right)\left(-7\right) = -7.$