Find the Inverse, If It Exists, of the Given Matrix $\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]$

Multiple Choice

Find the inverse, if it exists, of the given matrix.
- $\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]$

A) $\left[\begin{array}{rrr}-1 & 0 & 0 \\ -1 & -1 & 0 \\ -1 & -1 & -1\end{array}\right]$
B) $\left[\begin{array}{rrr}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]$
C) $\left[\begin{array}{rrr}1 & -1 & 1 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right]$
D) $\left[\begin{array}{rrr}1 & 0 & 0 \\ 1 & 1 & 0 \\ -2 & -1 & 1\end{array}\right]$