R-beta: qr(A)$rank

[Bertram Zinner]

I would like to find the rank of a matrix using R. Looking through a list 
of commands it seems that the command qr should do the job. Checking a 
simple example gave me the wrong answer. Here is the example: 

> A <- c(1,2,3,4,5,6)
> A <- matrix(A, nrow=2, ncol=3)
> A
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
> qr(A)$rank
[1] 3

The correct answer is two.

I should add that I am using the mac version of R. Any suggestions? --- 
Bertram
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