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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 =  ((a,b),(b,c) ) and B =  ((x),(y) )  AB =  ((a,b),(b,c) ) ((x),(y) ) =  (((ax + by)),((bx + cy)) )  BA =  ((x),(y) ) ((a,b),(b,c) ) impossible since   order (A) = 2 ×2  and order (B) = 2× 1

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

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