If A is a square matrix of order 3 such that |adj(A)|=64,then find |A| - Maths - Determinants

Question

If A is a square matrix of order 3 such that |adj(A)|=64,then find
|A|

Aakash Sharma · Accepted Answer

For any matrix

$| A \cdot Adj A | = | A | . I$

Thus for a matrix of order 3

$| A | \cdot | Adj A | = {| A |}^{3} \Rightarrow | Adj A | = \frac{| A |^{3}}{| A |} \Rightarrow 64 = | A |^{2} \Rightarrow | A | = \sqrt{64} = \pm 8$

If A is a square matrix of order 3 such that |adj(A)|=64,then find |A|.