Class 12 Maths Matrices 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:

  • 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.
  • 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

Solution:

 

 

 

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