In Example 1, change the element −7 to −5 and then find the inverse using the same method.

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.

A || 2 -3 4 -7