NCERT Class 12 · Ch 3 Exercise 3.2 · Q17
NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 17
Find k so that A²=kA−2I for A=\(\left[\begin{matrix}3 & -2\\4 & -2\end{matrix}\right]\).
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: k=1.
- Compute A²=\(\left[\begin{matrix}1 & -2\\4 & -4\end{matrix}\right]\).
- The (1,1) entry gives 1=3k−2, so k=1.
- At k=1, A−2I=\(\left[\begin{matrix}1 & -2\\4 & -4\end{matrix}\right]\) agrees with every entry of A².
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