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Question Number 96616 by mathocean1 last updated on 03/Jun/20

Answered by Rio Michael last updated on 03/Jun/20

$$A=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right)\mathrm{and}B=\left(\begin{array}{c}x\\ y\end{array}\right)$$$$AB=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}ax+by\\ bx+cy\end{array}\right)$$$$BA=\left(\begin{array}{c}x\\ y\end{array}\right)\left(\begin{array}{cc}a& b\\ b& c\end{array}\right)\mathrm{impossible}\mathrm{since}$$$$\mathrm{order}\left(\mathrm{A}\right)=2\times 2\mathrm{and}\mathrm{order}\left(\mathrm{B}\right)=2\times 1$$

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