For the matrix

Show that 

This verifies the method of Example 1.

Data from Example 1

Find the inverse of the matrix

First, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.

Now, we find the determinant of the original matrix, which means we evaluate

We now divide each element of the second matrix by −2. This gives

Checking by multiplication gives

Because AA⁻¹ = I, the matrix A⁻¹ is the proper inverse matrix.

P 9 D A =