CBSE Class 12 Mathematics 2025: question 22

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. $A^2=\left[\begin{array}{cc}2& 3\\ -1& 2\end{array}\right]\left[\begin{array}{cc}2& 3\\ -1& 2\end{array}\right]=\left[\begin{array}{cc}4-3& 6+6\\ -2-2& -3+4\end{array}\right]=\left[\begin{array}{cc}1& 12\\ -4& 1\end{array}\right]$

   1 mark

2. $A^2-4A+7I=\left[\begin{array}{cc}1& 12\\ -4& 1\end{array}\right]-\left[\begin{array}{cc}8& 12\\ -4& 8\end{array}\right]+\left[\begin{array}{cc}7& 0\\ 0& 7\end{array}\right]=\left[\begin{array}{cc}1-8+7& 12-12+0\\ -4+4+0& 1-8+7\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]=O$. Hence proved.

   1 mark

Answer: $A^2-4A+7I=O$ (verified)

Revise the chapter

• Chapter: Matrices (notes, formulas, where marks are lost and every past question)