Invertible Matrices
Invertible Matrices
If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse matrix of A and it is denoted by A – 1. In that case A is said to be invertible
Note: o A rectangular matrix does not possess inverse matrix, since for products BA and AB to be defined and to be equal, it is necessary that matrices A and B should be square matrices of the same order. o If B is the inverse of A, then A is also the inverse of B.
Theorem: Inverse of a square matrix, if it exists, is unique.
Numerical: Using elementary transformations, find the inverse of the matrices