The Inverse of a matrix exists only if the determinant is non zero. For every non singular matrix there exists a unique Inverse. If A is a matrix, then the inverse of the matrix is denoted by A-1. The product of a matrix and its Inverse equals the identity matrix I. There for we have the relation AA-1 = A-1A = I. Here inverse is obtained by applying elementary row transformations on the given matrix and similar changes are also made on an identity matrix of the same order. When the given matrix is transformed into an Identity Matrix the Identity Matrix becomes the Inverse Matrix.
Figure Given Below Shows a 3 X 3 Matrix.
Figure Given Below Shows the Inverse of the Given Matrix.
Figure Given Below Shows the Product of the Matrix and its Inverse.