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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 26 of 50
Marks: +1, -0
For the matrix X=(011101110),(X2−X)X=\begin{pmatrix}0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 0\end{pmatrix}, (X^2-X) is
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X2=(011101110)(011101110)X^2=\begin{pmatrix}0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 0\end{pmatrix}\begin{pmatrix}0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 0\end{pmatrix}
⇒X2=(211121112)\Rightarrow \qquad X^2=\begin{pmatrix}2 & 1 & 1\\ 1 & 2 & 1\\ 1 & 1 & 2\end{pmatrix}
⇒X2−X=(200020002)\Rightarrow \qquad X^2-X=\begin{pmatrix}2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{pmatrix}
=2(100010001)=2\begin{pmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{pmatrix}
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