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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 7 · Set 3 · Q22
If A= [1, 0; -1, 5], then find the value of K if A^2=6 A+K I_2, where I_2 is an identity matrix.
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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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.