Answer
$$
\left[ \begin{array}{ccc} 1&1&1\\ 0&-3&-4\\0&0&2\end{array} \right]=-6.
$$
Work Step by Step
Given
$$
\left[ \begin{array}{ccc} 1&1&1\\ 2&-1&-2\\1&-2&-1\end{array} \right].
$$
Now, adding $-2$ times the first row to the second row, adding $-1$ times the first row to the third row, we get
$$
\left[ \begin{array}{ccc} 1&1&1\\ 0&-3&-4\\0&-3&-2\end{array} \right].
$$
Adding $-1$ times the second row to the third row, we get
$$
\left[ \begin{array}{ccc} 1&1&1\\ 0&-3&-4\\0&0&2\end{array} \right].
$$
Hence, one can see easily that
$$
\left[ \begin{array}{ccc} 1&1&1\\ 0&-3&-4\\0&0&2\end{array} \right]=-6.
$$
