Let A be a 3 3 square matrix, such that A (adj A) = 2I, where I i… - Vidyadip

Question

Let A be a $3 \times 3$ square matrix, such that $A (adj\ A) = 2I,$ where I is the identity matrix. Write the value of $|adj\ A|.$

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Answer

$\because A(adj\ (A)) = |A|I2I = |A|I ($Given $A(adj\ A) = 2I)$
$|A| = 2$
Also, $|adj\ A| = |A|^{n-1}$
$= (2)^{3-1}$
$= (2)^2$
$= 4$
$|adj\ A| = 4$

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