Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{A}^{-1}=\left[\begin{array}{cr}1 & -2 \\ -2 & 2\end{array}\right]$, what is det (A)?
Options:
Solution:
1270 Upvotes
Verified Answer
The correct answer is:
$-\frac{1}{2}$
We know that det $(\mathrm{A})=\frac{1}{\operatorname{det}\left(\mathrm{A}^{-1}\right)}$
$\mathbf{A}^{-1}=\left[\begin{array}{rr}1 & -2 \\ -2 & 2\end{array}\right]$
$\Rightarrow\left|\mathrm{A}^{-1}\right|=\left|\begin{array}{rr}1 & -2 \\ -2 & 2\end{array}\right|=2-4=-2 \Rightarrow \operatorname{det}(\mathrm{A})=-\frac{1}{2}$
$\mathbf{A}^{-1}=\left[\begin{array}{rr}1 & -2 \\ -2 & 2\end{array}\right]$
$\Rightarrow\left|\mathrm{A}^{-1}\right|=\left|\begin{array}{rr}1 & -2 \\ -2 & 2\end{array}\right|=2-4=-2 \Rightarrow \operatorname{det}(\mathrm{A})=-\frac{1}{2}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.