If $\left[\begin{array}{lll}2 & 1 & 3\end{array}\right]\left(\begin{array}{ccc}-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)\left(\begin{array}{c}1 \\ 0 \\ -1\end{array}\right)=A$, then write the order of matrix $A$.
Consider, $\left(\begin{array}{lll}2 & 1 & 3\end{array}\right)\left(\begin{array}{ccc}-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)\left(\begin{array}{c}1 \\ 0 \\ -1\end{array}\right)=\mathrm{A}$
Order of matrix $(213)$ is $1 \times 3$.
Order of matrix $\left(\begin{array}{ccc}-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)$ is $3 \times 3$
Order of matrix $\left(\begin{array}{c}1 \\ 0 \\ -1\end{array}\right)$ is $3 \times 1$
Therefore, order of $(213)\left(\begin{array}{ccc}-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)\left(\begin{array}{c}1 \\ 0 \\ -1\end{array}\right)$ is $1 \times 1$.
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