Basic Technical Mathematics, 11th Edition

16.3 Finding the Inverse of a Matrix

• Inverse of a $\mathbf{2}\mathbf{\times \hspace{0.17em}}\mathbf{2}$ Matrix • Gauss–Jordan Method • Inverse on a Calculator

We now show how to find the inverse of a matrix, and in the next section, we show how it is used in solving a system of linear equations. First, we show two methods of finding the inverse of a $\mathbf{2}\mathbf{\times \hspace{0.17em}}\mathbf{2}$ matrix. The first method is as follows:

1. Interchange the elements on the principal diagonal.

2. Change the signs of the off-diagonal elements.

3. Divide each resulting element by the determinant of the given matrix.

CAUTION

This method can be used with second-order square matrices but not with higher-order matrices.

The following example illustrates this method.

EXAMPLE 1 Inverse of 2 × 2 matrix—method 1

Find the inverse of the matrix $A\hspace{0.17em}=\hspace{0.17em}\; ...$