In number theory we know that $$a^0=1$$ if $a \ne 0$
This we can prove using properties of indices as: if $m$ and $n$ are any two Non zero Real numbers
$$\frac{a^m}{a^n}=a^{m-n}$$
Putting $m=n$ we get $$a^0=\frac{a^m}{a^m}=1$$
But is this True in Matrices?
if i use same proof then i have to assume that $A$ is Invertible.
But is $$A^0=I$$ for any Non Null matrix whether it is Singular or Non Singular ?