If $A$ is a square matrix of order $3$ such that $| a d j . A | = 36$ , find $| A |$

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Solution

Using the formula =
$| a d j (A) | = | A |^{n - 1}$
where, $n =$ order of square matrix A
$∴$ Here
$| a d j (A) | = | A |^{3 - 1}$
$\Rightarrow 36 = | A |^{2}$
$\Rightarrow 6 = | A |$ .

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If A is a square matrix of order 3 such that |adj.A|=36, find |A|

Using the formula = |adj(A)|=|A|n−1where,n= order of square matrix A ∴ Here |adj(A)|=|A|3−1 ⇒36=|A|2 ⇒6=|A|.

If $A$ is a square matrix of order $3$ such that $| a d j . A | = 36$ , find $| A |$

Using the formula =
$| a d j (A) | = | A |^{n - 1}$
where, $n =$ order of square matrix A
$∴$ Here
$| a d j (A) | = | A |^{3 - 1}$
$\Rightarrow 36 = | A |^{2}$
$\Rightarrow 6 = | A |$ .