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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 4 · Set 1 · Q27
If A = [3, 2, 0; 1, 4, 0; 0, 0, 5], then compute A^2-7 A +10 I.
If $\displaystyle \mathrm{A}=\left[\begin{array}{lll}3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5\end{array}\right]$, then compute $\displaystyle \mathrm{A}^{2}-7 \mathrm{~A}+10 \mathrm{I}$.
Marking-scheme solution
$\displaystyle A^{2}=\begin{bmatrix} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{bmatrix}\begin{bmatrix} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{bmatrix}=\begin{bmatrix} 11 & 14 & 0 \\ 7 & 18 & 0 \\ 0 & 0 & 25 \end{bmatrix}$
$\displaystyle A^{2}-7 A+10 I=\begin{bmatrix} 11 & 14 & 0 \\ 7 & 18 & 0 \\ 0 & 0 & 25 \end{bmatrix}-\begin{bmatrix} 21 & 14 & 0 \\ 7 & 28 & 0 \\ 0 & 0 & 35 \end{bmatrix}+\begin{bmatrix} 10 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 10 \end{bmatrix}$
$\displaystyle A^{2}-7 A+10 I=\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.