6. (10%)

Use Gauss elimination to find the inverse of the following matrix $A$. First, reduce the matrix to row echelon form, and then continue to reduced row echelon form to obtain the inverse matrix.

$$A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 6 \\ 3 & 4 & 8 \end{bmatrix}$$