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.