Calculating the inverse

We saw on the previous page, AT-1 = A-1T. Or AT-1T = A-1. But the process of inverting a transpose is equivalent to doing column operations on the original matrix. So let's do some column operations.

Column operations only

We begin with the matrix from the previous page, augmented with an identity matrix of the appropriate rank and begin column operations.

Add column 2 to column 3.

Subtract column 1 from column 3.

Divide through column 3 by -2.

Subtract column 3 from column 1.

Equivalent inverse

The inverse performed this way is equivalent to the one calculated previously. A-1:

On the next page we'll combine column and row operations.