Question

For a invertible matrix $A$ if $A(\text{adj}A)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$, then $|A|=$

• A. 100
• B. - 100
• C. 10
• D. -10

Answer 1

Answer: (C)

Given : $A(\text{adj}A)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]=10\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=10I$
We know that, $A^{-1}=\frac{1}{|A|}\text{Adj}(A)$
$\Rightarrow A(\text{adj}A)=|A|I$
$\Rightarrow |A|=10$