Use the Inverse Formula $$A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]$$

Multiple Choice

Use the inverse formula $$A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]$$ to find the inverse of the 2×2 matrix (if it exists) . ​​ $$\left[ \begin{array} { l l } 2 & 3 \\1 & 5\end{array} \right]$$ ​

A) ​ $$\frac { 1 } { 7 } \left[ \begin{array} { l l } 5 & 3 \\1 & 2\end{array} \right]$$
B) ​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } - 5 & - 3 \\1 & 2\end{array} \right]$$
C) ​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } - 5 & 3 \\1 & - 2\end{array} \right]$$
D) ​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } 5 & - 3 \\- 1 & 2\end{array} \right]$$
E) ​ $$\frac { 1 } { 7 } \left[ \begin{array} { l l } - 5 & - 3 \\- 1 & - 2\end{array} \right]$$