Suppose T Rn rightarrow Rn is an invertible linear transfor

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

Since T is invertible, then A will also be invertible.

therefore when we get reduced echelon form of A it will be identity matrix( because being invertible it determinat should be non zero.)

Therefore, the reduced echelon form of A is I of order n.