Vector/matrix algebra

I have made the following vector and matrix:

>> v =[2,1]'

v =

2
1

>> A = [1,2;-1,3;4,4;5,2]

A =

1 2
-1 3
4 4
5 2


In this case A*v is the same as v'*A' (where ' means transposed):

>> A*v

ans =

4
1
12
12

>> v'*A'

ans =

4 1 12 12

>>



If A*v is defined does it always give the same result as v'*A'?
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