Question

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

• A. 125
• B. 25
• C. 10
• D. 5

Answer 1

Answer: (B)

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