Suppose T Rn rightarrow Rn is an invertible linear transform

Suppose T: R^n rightarrow R^n is an invertible, linear transformation with standard matrix A. What can you say about the reduced echelon form of A? Explain without using the IMT.

Solution

The row reduced echolen form must have no row with all zero elements . There must be one non zero elemnt in each row since the matrix is invertible