Find the inverse of each of the given matrices by the method of Example 1 of this
Find the inverse of each of the given matrices by the method of Example 1 of this section.
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.
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