## If a Matrix $A$ is Full Rank, then $\rref(A)$ is the Identity Matrix

## Problem 645

Prove that if $A$ is an $n \times n$ matrix with rank $n$, then $\rref(A)$ is the identity matrix.

Here $\rref(A)$ is the matrix in reduced row echelon form that is row equivalent to the matrix $A$.

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