Compute the Determinant of the Matrix $2 \times 2$ Matrix to Calculate the Inverse of the Given Matrix

Compute the determinant of the matrix. If the determinant is nonzero, use the formula for inverting a $2 \times 2$ matrix to calculate the inverse of the given matrix. $\left[ \begin{array} { c c } 1 & 2 \\2 & - 1\end{array} \right]$

A) -5; $\left[ \begin{array} { c c } \frac { 1 } { 5 } & \frac { 2 } { 5 } \\\frac { 2 } { 5 } & - \frac { 1 } { 5 }\end{array} \right]$

B) -10; $\left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 2 } { 5 } \\\frac { 2 } { 5 } & \frac { 1 } { 5 }\end{array} \right]$

C) 5; $\left[ \begin{array} { l } - \frac { 1 } { 5 } - \frac { 2 } { 5 } \\- \frac { 2 } { 5 } \quad \frac { 1 } { 5 }\end{array} \right.$

D) -4; $\left[ \begin{array} { l } - \frac { 1 } { 5 } - \frac { 2 } { 5 } \\- \frac { 2 } { 5 } \quad \frac { 1 } { 5 }\end{array} \right.$

E) -10; $\left[ \begin{array} { c c } \frac { 1 } { 5 } & \frac { 2 } { 5 } \\\frac { 2 } { 5 } & - \frac { 1 } { 5 }\end{array} \right]$