It is defined as the matrix that is obtained by interchanging rows with columns or columns with rows. This will not only change the size of the matrix but also the indices of every element. However, the indices of the diagonal elements remain the same.
- Image Courtesy: katjaas.nl
A matrix ‘X’ is said to be an inverse matrix if there is another matrix ‘Y’ such that it satisfies this equation: XY=YX=I. X will be called the inverse matrix of Y and Y will be called the inverse matrix of X. In addition to this there is a necessary and sufficient condition that matrix X must satisfy in order to be invertible. This necessary and sufficient condition is that the determinant of matrix X must be non zero.
- Image Courtesy: mathsisfun.com