# 1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

let A be a square matrix of order n.
$A\left(adjA\right)=|A|{I}_{n}$ , where
therefore

given |A| = 5 and n = 3
therefore
$\left|A\left(adjA\right)\right|={5}^{3}\phantom{\rule{0ex}{0ex}}=125$
hope this helps you.

• 10

|A adj A| = |A| n-1 here n(order) = 3 therefore |A adj .A| = 5 3-1 = 52 = 25. Hope it helps.

• -6
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