[tex]\displaystyle (A-B^{-1})B-(AD+CB)+CD=O_2 \\ \\ AB-I_2-AD-CB+CD=O_2 \\ \\ AB-AD-CB+CD=I_2 \\ \\ A(B-D)-C(B-D)=I_2 \\ \\ (A-C)(B-D)=I_2 \\ \\ O~relatie~de~forma~XY=I_2~ne~spune~ca~X~si~Y~sunt~inverse,~adica \\ \\ Y=X^{-1}.~Deci~are~loc~si~YX=I_2. \\ \\ (B-D)(A-C)=I_2 \\ \\ BA-BC-DA+DC=I_2 \\ \\ DC-I_2+BA=BC+DA \\ \\ Varianta~b).[/tex]
