The multiplicative inverse of a square matrix is called its inverse matrix. If a matrix A has an inverse, then A is said to be nonsingular or invertible. A singular matrix does not have an inverse. To find the inverse of a square matrix A , you need to find a matrix A-1 such that the product of A and A-1 is the identity matrix.
In other words, for every square matrix A which is nonsingular there exist an inverse matrix, with the property that, AA-1 = A-1A = I , where I is the identity matrix of the appropriate size.
You can use either of the following method to find the inverse of a square matrix.
Let A be an matrix.
You may use the following formula when finding the inverse of matrix.
If A is non-singular matrix, there exists an inverse which is given by , where is the determinant of the matrix.
Find A-1 , if it exists. If A-1 does not exist, write singular.
Write the doubly augmented matrix [ A | In].
Apply elementary row operations to write the matrix in reduced row-echelon form.
The system has a solution.
Therefore, A is invertible and