Model fitting by least squares

Inverse of a $2\times 2$ matrix

$$\bold A ^{-1} \quad\quad\quad\quad \bold A \quad\quad = \ \quad\bold I$$ (110)

$$\frac{1}{ad-bc} \left[ \begin{array}{rr} d & -b \\ -c & a \end{array}\right] \quad \left[ \begin{array}{rr} a & b \\ c & d \end{array}\right] = \left[ \begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right]$$ (111)