\title	{inversa por la izquierda 2x2}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{tex}

\integer{range=20}
\integer{sign1=random(1,-1)}
\integer{sign2=random(1,-1)}
\integer{a0=random(0..\range)}
\integer{b0=random(1..\range)}
\integer{c0=random(1..\range)}
\integer{d0=random(0..\range)}
\integer{a1=\a0*(\sign1)}
\integer{b1=\b0*(\sign1)}
\integer{c1=-(\c0)*(\sign2)}
\integer{d1=\d0*(\sign2)}
\integer{a2=random(-\range..\range)}
\integer{b2=random(-\range..\range)}
\integer{c2=random(-\range..\range)}
\integer{d2=random(-\range..\range)}
\integer{a3=(\a1)*(\a2)+(\b1)*(\c2)}
\integer{b3=(\a1)*(\b2)+(\b1)*(\d2)}
\integer{c3=(\c1)*(\a2)+(\d1)*(\c2)}
\integer{d3=(\c1)*(\b2)+(\d1)*(\d2)}

\statement{Determinar la matriz $A=\pmatrix{a&b\cr c&d}$ tal que
 $$ \pmatrix{\a1&\b1\cr\c1&\d1} \pmatrix{a&b\cr c&d}
 = \pmatrix{\a3&\b3\cr\c3&\d3} .$$}
\answer{a=\a2}
\answer{b=\b2}
\answer{c=\c2}
\answer{d=\d2}