$\left[\begin{array}{ccc} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]\left[\begin{array}{ccc} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right]$
= $\left[\begin{array}{lll} {1(-1)+2(0)+3(2)} & {1(1)+2(-1)+3(3)} & {1(0)+2(1)+3(4)} \\ {0(-1)+1(0)+0(2)} & {0(1)+1(-1)+0(3)} & {0(0)+1(1)+0(4)} \\ {1(-1)+1(0)+0(2)} & {1(1)+1(-1)+0(3)} & {1(0)+1(1)+0(4)} \end{array}\right]$
= $\left[\begin{array}{ccc} {5} & {8} & {14} \\ {0} & {-1} & {1} \\ {-1} & {0} & {1} \end{array}\right]$
Now, $\left[\begin{array}{ccc} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right]\left[\begin{array}{lll} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]$
= $\left[\begin{array}{ccc} {-1(1)+1(0)+0(1)} & {-1(2)+1(1)+0(1)} & {-1(3)+1(0)+0(0)} \\ {0(1)+(-1)(0)+1(1)} & {0(2)+(-1)(1)+1(1)} & {0(3)+)(-1)(0)+1(0)} \\ {2(1)+3(0)+4(1)} & {2(2)+3(1)+4(1)} & {2(3)+3(0)+4(0)} \end{array}\right]$
= $\left[\begin{array}{ccc} {-1} & {-1} & {-3} \\ {1} & {0} & {0} \\ {6} & {11} & {6} \end{array}\right]$
Therefore, $\left[\begin{array}{ccc} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]\left[\begin{array}{ccc} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right] \neq\left[\begin{array}{ccc} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right]\left[\begin{array}{ccc} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]$
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