Prove that the commutative property holds on the matrix multiplication.
Taking into account that
(1−101)(−1101)=(−1001),\begin{pmatrix} 1 & -1\\ 0 & 1 \end{pmatrix} \begin{pmatrix} -1 & 1\\ 0 & 1 \end{pmatrix} = \begin{pmatrix} -1 & 0\\ 0 & 1 \end{pmatrix},(10−11)(−1011)=(−1001), but
(−1101)(1−101)=(−1201),\begin{pmatrix} -1 & 1\\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & -1\\ 0 & 1 \end{pmatrix} = \begin{pmatrix} -1 & 2\\ 0 & 1 \end{pmatrix},(−1011)(10−11)=(−1021),
we conclude that the commutative property does not hold on the matrix multiplication.
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