Question

If $A(adj A)= 5I$, where $I$ is identity matrix of order 3, then $|adj A | $=

• A. 125
• B. 25
• C. 10
• D. 5

Answer 1

Answer: (B)

$A\, (adj\: A)= 5 I$
We know that $A \, (adj\: A)= |A | I= 5 I$ $\therefore \, |A| =5,$
$I$ is identity matrix of order= order of matrix $A$
$\therefore $ Order of matrix $A = 3$
We know, $|adj \, A| = |A|^{-1}$
where $n$ is the order of matrix $A$
$\therefore \, |adj \: A | = (5)^{3-I} = 5^2 = 25$