Question Number 39013 by Rio Mike last updated on 01/Jul/18
$${Given}\:{the}\:{matrices} \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{4}}\end{pmatrix}\:{and}\:{I}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{matrix}\:{B}\:{if}\: \\ $$$${BA}=\:{I} \\ $$$${find}\:{A}'\:{the}\:{reflection}\:{on}\:{the} \\ $$$${line}\:{y}\:=\:{x}\:{and}\:{A}''\:{the}\:{enlargement} \\ $$$${with}\:{matrix}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}. \\ $$
Commented by mondodotto@gmail.com last updated on 02/Jul/18
$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{A}}×\boldsymbol{\mathrm{B}}=\mathrm{I}\Rightarrow\mathrm{identity}\:\mathrm{matrix} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{B}}\:=\:\boldsymbol{\mathrm{inverse}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{matrix}}\:\boldsymbol{\mathrm{A}} \\ $$