A question in my textbook, asks the following:
Determine, with proof, whether the following subset of $M(n,n)$ is a subspace: The subset of matrices that are in row echelon form.
To clarify (in case this notation is non standard) $M(n,n)$ is the set of all $n\times n$ matrices.
The answers in the rear of the textbook indicate it is NOT a subspace, but provides zero reasoning. Any help or insight would be appreciated. Thank you.