Determinants and matrices

$$\left[ {\begin{array}{*{20}{c}} {10} \\ { - v{{a}^{{ - 1}}}1} \\ \end{array} } \right]\left[ {\begin{array}{*{20}{c}} {au} \\ {vb} \\ \end{array} } \right]\left[ {\begin{array}{*{20}{c}} {1 - {{a}^{{ - 1}}}u} \\ {01} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}{c}} {a0} \\ {0b - v{{a}^{{ - 1}}}u} \\ \end{array} } \right]$$ (1.1) provided a is regular.