Is the empty matrix $M$ ($m \times n$) with $m$ or $n$ equal to zero in RREF ? Does it posses every matrix property one would wish?

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Is the empty matrix $M$ ($m \times n$) with $m$ or $n$ equal to zero in RREF ?

Reading a proof in Linear Algebra induction starts off by proving $P(n)$ holds for $n=0$, where $P(n)$ is the statement: "The matrix $M$ ($m \times n$) has a reduced row echelon form".

However, no introduction has been given to the empty matrix $A$. Is the empty matrix considered to have every matrix property one would wish, like inverse, RREF-form etc. ?