Question

if A is a square matrix of order 4 such that |adj A|=125 then |A| is ?​

Answer 1

The value of |A| when |adjA| = 125 is 5.

Step-by-step explanation:

Given, A is a square matrix of order 4 and |adj A| = 125

and using the properties of adjacent  matrixes

|adj A| = $|A|^{n-1}$

 and as n= 4, then

   |adjA| =$|A|^{4-1}$

    125   =  $|A|^{3}$

        $5^3 = |A|^{3}$

         5 = |A|

hence, the value of |A| is 5.