Question

The inverse of the matrix $\begin{bmatrix} {5}&{-2}\\ {3}&{1}\\ \end{bmatrix}$ is is

• A. $\frac {1}{11}\begin{bmatrix} {1}&{2}\\ {-3}&{5}\\ \end{bmatrix} $
• B. $\begin{bmatrix} {1}&{2}\\ {-3}&{5}\\ \end{bmatrix} $
• C. $\frac {1}{13}\begin{bmatrix} {-2}&{5}\\ {1}&{3}\\ \end{bmatrix} $
• D. $\begin{bmatrix} {1}&{3}\\ {-2}&{5}\\ \end{bmatrix} $

Answer 1

The Correct Option is A

Let $A=\begin{bmatrix}5 & -2 \\ 3 & 1\end{bmatrix}$ $|A|=5+6=11$ and $adj\, A=\begin{bmatrix}1 & 2 \\ -3 & 5\end{bmatrix}$ $A^{-1}=\frac{1}{|A|}$ (adj A) $=\frac{1}{11}\begin{bmatrix}1 & 2 \\ -3 & 5\end{bmatrix}$