« Matrix Addition and Multiplication 

To find the inverse of matrix A, using GaussJordan elimination, we must find a sequence of elementary row operations that reduces A to the identity and then perform the same operations on I_{n} to obtain A^{1}.
Example 1: Find the inverse of
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Step 2: Apply row operations to this matrix until the left side is reduced to I. The computations are:
Step 3: Conclusion: The inverse matrix is:
If A is not invertible, then, a zero row will show up on the left side.
Example 2: Find the inverse of
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Step 2: Apply row operations
Step 3: Conclusion: This matrix is not invertible.
Example 1: Find the inverse of
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Step 2: Apply row operations to this matrix until the left side is reduced to I. The computations are:
Step 3: Conclusion: The inverse matrix is: