Find the matrix ${\mathrm{A}}^{2}$, where $\mathrm{A}=\left[{a}_{ij}\right]$ is a $2\times 2$ matrix whose elements are given by ${a}_{ij}=maximum(\mathrm{i},\mathrm{j})-minimum(\mathrm{i},\mathrm{j})$ :

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YESPYQ · Accepted Answer

Correct answer: c) $\left[\begin{matrix}1 & 0 \ 0 & 1\end{matrix}\right]$. Given: ${a}_{ij}=\max (i,j)-\min (i,j)$ So, ${a}_{11}=\max (1,1)-\min (1,1)=1-1=0,\ {a}_{12}=\max (1,2)-\min (1,2)=2-1=1,\ {a}_{21}=\max (2,1)-\min (2,1)=2-1=1,\ {a}_{22}=\max (2,2)-\min (2,2)=2-2=0$ The matrix $A$ is: $A=\left[\begin{matrix}0 & 1 \ 1 & 0\end{matrix}\right]$ Hence, ${A}^{2}=A\times A\ =\left[\begin{matrix}0 & 1 \ 1 & 0\end{matrix}\right]\times \left[\begin{matrix}0 & 1 \ 1 & 0\end{matrix}\right]\ =\left[\begin{matrix}1 & 0 \ 0 & 1\end{matrix}\right]$

Find the matrix \({\mathrm{A}}^{2}\), where \(\mathrm{A}=\left[{a}_{ij}\right]\) is a \(2\times 2\) matrix whose element…

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