CUET · MATHS · PYQ PAPER 2023
If \(A = \begin{bmatrix} 2a & 0 & 0 \\ 0 & 2a & 0 \\ 0 & 0 & 2a \end{bmatrix}\), then the value of \(|\text{adj A}|\) is:
- A \(64a^6\)
- B \(8a^3\)
- C \(64a^3\)
- D \(8a^6\)
Answer & Solution
Correct Answer
(A) \(64a^6\)
Step-by-step Solution
Detailed explanation
\( |A| = \det \begin{vmatrix} 2a & 0 & 0 \\ 0 & 2a & 0 \\ 0 & 0 & 2a \end{vmatrix} = (2a)^3 = 8a^3 \) \( |\text{adj A}| = |A|^{n-1} = |A|^{3-1} = |A|^2 \) \( |\text{adj A}| = (8a^3)^2 = 64a^6 \)
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