CBSE 2025 · Region 7 · Set 3 · Q22 · 2 marks
If $\displaystyle A=\left[\begin{array}{rr}1 & 0 \\ -1 & 5\end{array}\right]$, then find the value of $\displaystyle K$ if $\displaystyle A^{2}=6 A+K I_{2}$, where $\displaystyle I_{2}$ is an identity matrix.
Marking-scheme solution
\[A^{2}=6 A+K I_{2} \Rightarrow\left[\begin{array}{cc}
1 & 0 \\
-6 & 25
\end{array}\right]=\left[\begin{array}{cc}
6+K & 0 \\
-6 & 30+K
\end{array}\right]
\]
$\displaystyle \Rightarrow 6+K=1 \Rightarrow K=-5$, also satisfies $\displaystyle 30+K=25$.
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