To find the inverse of a matrix A using elementary transformations, we can use elementary row operations on A = IA, in a sequence, until we get I = BA. We can also use elementary column operations on A = AI, in a sequence, till we get I = AB. If the inverse of matrix A exists, we can write A = IA and apply a sequence of row operations till we get an identity matrix on the LHS and use the same elementary operations on the RHS to get I = BA