CUET · MATHS · PYQ PAPER 2023
If \(A=\left[\begin{array}{cc}2 & -3 \\ 3 & 4\end{array}\right]\) then, the value of \(A^2-6 A\)
- A 6I, Where I is an identity matrix of order 2
- B 6I, Where I is an identity matrix of order 2
- C 17I, Where I is an identity matrix of order 2
- D \(-17 I\),, Where I is an identity matrix of order 2
Answer & Solution
Correct Answer
(D) \(-17 I\),, Where I is an identity matrix of order 2
Step-by-step Solution
Detailed explanation
\( \text{tr}(A) = 2 + 4 = 6 \) \( \det(A) = (2)(4) - (-3)(3) = 8 + 9 = 17 \) \( A^2 - \text{tr}(A)A + \det(A)I = 0 \) \( A^2 - 6A + 17I = 0 \) \( A^2 - 6A = -17I \)
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