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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 4 · Set 3 · Q21
If A = [2, -2; -2, 2] and A^2= kA, then find the value of k.
If $\displaystyle \mathrm{A}=\left[\begin{array}{rr}2 & -2 \\ -2 & 2\end{array}\right]$ and $\displaystyle \mathrm{A}^{2}=\mathrm{kA}$, then find the value of k .
Marking-scheme solution
\[\begin{aligned}
& \mathrm{A}=\left[\begin{array}{cc}
2 & -2 \\
-2 & 2
\end{array}\right] \Rightarrow \mathrm{A}^{2}=\left[\begin{array}{cc}
8 & -8 \\
-8 & 8
\end{array}\right] \\
& \mathrm{A}^{2}=k \mathrm{A} \Rightarrow\left[\begin{array}{cc}
8 & -8 \\
-8 & 8
\end{array}\right]=\left[\begin{array}{cc}
2 k & -2 k \\
-2 k & 2 k
\end{array}\right] \\
& \Rightarrow k=4
\end{aligned}
\]
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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.