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) . $\left[ \begin{array} { c c } 6 & 7 \\- 5 & 13\end{array} \right]$

A) $\frac { 1 } { 113 } \left[ \begin{array} { c c } 13 & - 7 \\5 & 6\end{array} \right]$
B) $\frac { 1 } { 113 } \left[ \begin{array} { c c } - 13 & 7 \\5 & - 6\end{array} \right]$
C) $\frac { 1 } { 113 } \left[ \begin{array} { c c } - 13 & - 7 \\5 & 6\end{array} \right]$
D) $\frac { 1 } { 113 } \left[ \begin{array} { c c } 13 & 7 \\5 & 6\end{array} \right]$
E) $\frac { 1 } { 113 } \left[ \begin{array} { c c } - 13 & - 7 \\- 5 & - 6\end{array} \right]$