Question Number 80340 by Rio Michael last updated on 02/Feb/20
$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$
Answered by MJS last updated on 02/Feb/20
$$\mathrm{if}\:{QP}\:\mathrm{means}\:\mathrm{first}\:{Q}\:\mathrm{then}\:{P} \\ $$$${a}\rightarrow{b}\rightarrow{d} \\ $$$${b}\rightarrow{a}\rightarrow{c} \\ $$$${c}\rightarrow{d}\rightarrow{b} \\ $$$${d}\rightarrow{c}\rightarrow{a} \\ $$$${QP}=\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{d}}&{{c}}&{{b}}&{{a}}\end{pmatrix} \\ $$