Mathematics - Matrices Question with Solution | TestHub

$|{\mathrm{A}}^{1003}-5{\mathrm{A}}^{1002}|=|{\mathrm{A}}^{1002}(\mathrm{A}-5\mathrm{I})|$

$=|{\mathrm{A}}^{1002}||\mathrm{A}-5\mathrm{I}|$

$=|\mathrm{A}{|}^{1002}|\mathrm{A}-5\mathrm{I}|$

$=1\times \left|\begin{array}{cc}0& -6\\ 1& -6\end{array}\right|=6$