Dimension of a matrix vectorspace

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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...
 
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That seems correct.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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