Hi there just something I'm a bit unsure of and want it cleared up if you can help me please?

So in my book it gives a 3x5 matrix, and it tells me that rank(A) is always less than or equal to 3, can this be generalised to amxnmatrix, with rank less than or equal to n, where m>n, and rank less than or equal to m, if m<n?

Also, I don't understand how the rank can be zero? Would this not mean that there are no vectors in the basis; is this possible?