In number arithmetic every number ( ) has a reciprocal written as or such that . Some, but not all, square matrices have inverses. If a square matrix has an inverse, , then
We develop a rule for finding the inverse of a matrix (where it exists) and we look at two methods of finding the inverse of a matrix (where it exists).
Non-square matrices do not possess inverses so this Section only refers to square matrices.
- be familiar with the algebra of matrices
- be able to calculate a determinant
- know what a cofactor is
- state the condition for the existence of an inverse matrix
- use the formula for finding the inverse of a matrix
- find the inverse of a matrix using row operations and using the determinant method
2 The inverse of a 2 2 matrix
3 The inverse of a 3 3 matrix - Gauss elimination method
4 The inverse of a 3 3 matrix - determinant method