Math Problem Solver

If the determinant is non-zero, that is if $- n^{3} v^{3} i \ne 0$, then the inverse is: $$\left[\begin{matrix}\frac{3 i}{n v} & - \frac{3 i}{n v} & \frac{i}{n v}\\- \frac{8 i}{n v} & \frac{12 i}{n v} & - \frac{5 i}{n v}\\\frac{4 i}{n v} & - \frac{7 i}{n v} & \frac{3 i}{n v}\end{matrix}\right]$$ The inverse of a square matrix $A$, is the matrix $A^{-1}$ such that: $$A^{-1} A = A A^{-1} = I$$ where $I$ is the identity matrix.