find the inverse of matrix by gauss jordan method
$$\begin{bmatrix} -1 & 2 & 2 \\\\ 2 & -1 & 2 \\\\ 2 & 2 & -1 \end{bmatrix}$$
MathBot Answer:
The inverse is: \[ \left[\begin{matrix}- \frac{1}{9} & \frac{2}{9} & \frac{2}{9}\\\frac{2}{9} & - \frac{1}{9} & \frac{2}{9}\\\frac{2}{9} & \frac{2}{9} & - \frac{1}{9}\end{matrix}\right] \] 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.