Find the Inverse of the Matrix A, If It Exists $$A = \left[ \begin{array} { r r r } 5 & - 1 & 5 \\5 & 0 & 3 \\10 & - 1 & 8\end{array} \right]$$

Multiple Choice

Find the inverse of the matrix A, if it exists.
- $$A = \left[ \begin{array} { r r r } 5 & - 1 & 5 \\5 & 0 & 3 \\10 & - 1 & 8\end{array} \right]$$

A) $A ^ { - 1 } = \left[ \begin{array} { c c c } 1 & 0 & \frac { 3 } { 5 } \\ 0 & 1 & - 2 \\ 0 & \frac { 4 } { 5 } & 0 \end{array} \right]$
B) $A ^ { - 1 } = \left[ \begin{array} { r r r } 1 & 0 & \frac { 3 } { 5 } \\ 0 & 1 & - 2 \\ 0 & 0 & 0 \end{array} \right]$
C) $A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & 5 & 10 \\ - 1 & 0 & - 1 \\ 5 & 3 & 8 \end{array} \right]$
D) $A ^ { - 1 }$ does not exist.