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Choose the correct option.
If A is a 3 × 3 matrix such that A(adj A) = (3 0 0; 0 3 0; 0 0 3), then the value of |Aᵀ| will be
If $A$ is a $3 \times 3$ matrix such that $A(\text{adj } A) = \begin{pmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{pmatrix}$, then the value of $|A^T|$ will be
- (a)$27$
- (b)$9$
- (c)$3$
- (d)$-3$
Answer
Answer
Correct option: (c)
Answer: (c) $3$
$A(\text{adj } A) = |A| I = 3I$, so $|A| = 3$.
Hence $|A^T| = |A| = 3$.