Answer
$$\left[ \begin {array}{ccc} -1&-1&-3\\0& -1&-2\\0&0&1
\end {array} \right].$$
Work Step by Step
Let $A$ be a matrix given by
$$A =\left[ \begin {array}{ccc} 1&-1&1\\ 0& 1&2\\0&0&-1
\end {array} \right].$$
Now, the cofactor matrix of $A$ can be calculated by
$$\left[ \begin {array}{ccc} -1&0&0\\ -1& -1&0\\-3&-2&1
\end {array} \right]$$
hence the adjoint matrix of $A$ is given by
$$\left[ \begin {array}{ccc} -1&-1&-3\\0& -1&-2\\0&0&1
\end {array} \right].$$
