Give an example that the commutative law does not holds on the matrix multiplication.
Since
(2−201)(−1201)=(−2201),\begin{pmatrix} 2 & -2\\ 0 & 1 \end{pmatrix} \begin{pmatrix} -1 & 2\\ 0 & 1 \end{pmatrix} = \begin{pmatrix} -2 & 2\\ 0 & 1 \end{pmatrix},(20−21)(−1021)=(−2021), but
(−1201)(2−201)=(−2401),\begin{pmatrix} -1 & 2\\ 0 & 1 \end{pmatrix} \begin{pmatrix} 2 & -2\\ 0 & 1 \end{pmatrix} = \begin{pmatrix} -2 & 4\\ 0 & 1 \end{pmatrix},(−1021)(20−21)=(−2041),
we conclude that the commutative property does not hold on the matrix multiplication.
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