Question

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

• A. $100$
• B. $-100$
• C. $10$
• D. $-10$

Answer 1

The correct option is C $10$

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