Question #248991

Give an example that the commutative law does not holds on the matrix multiplication.


1
Expert's answer
2021-10-11T15:55:39-0400

Since


(2201)(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}, but


(1201)(2201)=(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},


we conclude that the commutative property does not hold on the matrix multiplication.


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