Matrix Inverse Using Elementary Row Transformations

We are given the matrix and need to find its inverse using elementary row transformations. The augmented matrix for this operation is:

Step 1: Make the first element in the first column equal to 1. \\ We divide the first row by (assuming ): The augmented matrix becomes: Step 2: Make the first element in the second column equal to 0. \\ We subtract times the first row from the second row: The augmented matrix becomes: Step 3: Make the second element in the second column equal to 1. \\ We divide the second row by : The augmented matrix becomes: Step 4: Make the second element in the first column equal to 0. \\ We add times the second row to the first row: The augmented matrix becomes: Thus, the inverse of the matrix is:

Final Answer: