Question Number 96616 by mathocean1 last updated on 03/Jun/20
Answered by Rio Michael last updated on 03/Jun/20
$${A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{and}\:{B}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix} \\ $$$${AB}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{ax}\:+\:{by}}\\{{bx}\:+\:{cy}}\end{pmatrix} \\ $$$${BA}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{impossible}\:\mathrm{since}\: \\ $$$$\mathrm{order}\:\left(\mathrm{A}\right)\:=\:\mathrm{2}\:×\mathrm{2}\:\:\mathrm{and}\:\mathrm{order}\:\left(\mathrm{B}\right)\:=\:\mathrm{2}×\:\mathrm{1} \\ $$