4.7 Inverse Matrix
1. If A is a square matrix, B is another square matrix and A × B = B × A = I, then matrix A is the inverse matrix of matrix B and vice versa. Matrix A is called the inverse matrix of B for multiplication and vice versa.
2. The symbol A-1 denotes the inverse matrix of A.
3. Inverse matrices can only exist for square matrices but not all square matrices have inverse matrices.
4. If AB ≠ I or BA ≠ I, then A is not the inverse of B and B is not the inverse of A.
Example 1:Determine whether matrix is an inverse matrix of matrix
5. The inverse of a matrix may also be found using a formula.
If , then the inverse matrix of A, A-1, is given by the formula below.
6. ad – bc is known as the determinant of matrix A.
7. If the determinant, ad – bc = 0, then the inverse matrix of A does not exist.
Example 2:Find the inverse matrix of using the formula.
Example 3:The inverse matrix of Find the value of r, of s and of t.