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We are given a matrix: $$ A = \begin{bmatrix} 3 & 1 & 2 \\ -2 & 3 & -5 \\ 1 & 2 & 4 \end{bmatrix} $$ We will find the inverse of matrix $A$ using the Gauss-Jordan method, which involves transforming the augmented matrix $[A | I]$ into $[I | A^{-1}]$, where $I$ is the identity matrix. --- ### Step 1: Write the augmented matrix $[A | I]$ $$ \left[\begin{array}{ccc|ccc} 3 & 1 & 2 & 1 & 0 & 0 \\ -2 & 3 & -5 & 0 & 1 & 0 \\ 1 & 2 & 4 & 0 & 0 & 1 \\ ____ ___ _______ _________ _______ _________ ______ _________ _________ __________ ____.
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