If A is an invertible matrix of order 3 and |A| = 5, then find |adj. A|.

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Question

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If A is an invertible matrix of order 3 and |A| = 5, then find |adj. A|.

Solution

$|adj A| = {|A|}^{n - 1},$ where n is order of square matrix

Given A is an invertible matrix of order 3

$|adj A| = {|A|}^{3 - 1} = {|A|}^{2} Since, |A| = 5 ∴ |adj A| = {(5)}^{2} = 25$

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