If A = [ * 20 c 1&3 2&1 ], then determinant of A^2 - 2A is - Vidyadip

Question

If $A = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]$, then determinant of ${A^2} - 2A$ is

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Answer

b
(b) $A = \left| {\,\begin{array}{*{20}{c}}
1&3\\
2&1
\end{array}\,} \right| $

${A^2} = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}7&6\\4&7\end{array}} \right]$

and ${A^2} - 2A = \left[ {\begin{array}{*{20}{c}}5&0\\0&5\end{array}} \right]\,,{\rm{det }}({A^2} - 2A) = \left| {\,\begin{array}{*{20}{c}}5&0\\0&5\end{array}\,} \right| = 25$.

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