Dimension of a matrix vectorspace

[Locoism]

Homework Statement

Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F .

The Attempt at a Solution

The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be n*m? For the basis (it has m*n elements), would it simply be zero matrices with a 1 in the "ij" entry, starting at 1,1 and ending at n,m?
I feel like the question is just too easy, which is leading me to doubt my answer...

 

[micromass]

That seems correct.