# $A$ has $4$ rows, $3$ columns -- for which $m,n$ is $A \in M_{m,n}(\Bbb R)$?

This may sound silly but I have a matrix with 4 rows and 3 columns. This matrix is labelled $A$.

The question says:

Find $m, n$ such that $A \in M_{m,n}(\Bbb R)$

Now is $m$ just 4 and $n$ is 3? Apologies if this is obvious, just wanted to make sure this was the correct notation since for example $a_{34}$ would denote the element in the third row and fourth column of a matrix.

Your assertion is correct (and your $A$ does not posess an element $a_{34}$). Other notations include $$M_{m,n} (\mathbb R), \mathbb R^{m\times n}, \mathbb R^{(m,n)}, {\rm Mat}_{m,n}(\mathbb R)$$ And most of the time, $m$ is the number of rows and $n$ is the number of columns (not all the time, duh)
$A\in M_{4,3}(\mathbb{R})$ and yes, for the second question.