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\section{Inverse}  For a 3x3 non-singular matrix $A$ with a determinant $|A|$  defined by  \begin{equation} A=\begin{bmatrix}   a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}  \end{bmatrix}  \end{equation}  we can calculate the inverse defined by as  \begin{equation} A^{-1}=\frac{1}{|A|}  \begin{bmatrix}