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) $\frac { 1 } { 7 } \left[ \begin{array} { l l } - 5 & - 3 \\- 1 & - 2\end{array} \right]$