The product of a matrix and its inverse will be an identitymatrix of the same dimensions where all of the values are zero excluding a diagonal line of ones. It looks similar to this:

Let's Practice: Given below are two methods to find the inverse of a matrix O.

If , find

Using Row Operations:

The following are the steps than can be taken to change a matrix into reduced row echelon form (rref):

Multiply a row by a scalar quantity.

Switching one row’s position with another.

Adding one multiple of a row to another multiple of a row.

Create an augmented matrix with the original matrix on the left and an identitymatrix on the right. The dotted line is just there to distinguish between the different sides.

Type “3”, |ENTER|, “3”, |ENTER|. This will set the dimensions of the matrix.

You are now ready to insert the entries of matrix O from the previous example. Type each value starting from the top-left working right, pressing |ENTER| will tab to the next position.