Fixed effect design matrix must be of full column rank--even though it is?

Hi!

I want to predict a continuous variable "rating" with a linear mixed model. Ratings are done by two different groups of people (exp and control). People in the experimental group do the rating twice in two different blocks. I therefore have the between subject factor group and a within factor ( block). I set up the design matrix as follows (here on random data)

rating=rand(40,1); group=[ones(20,1); repmat(2,20,1)];
block=[zeros(20,1); repmat(1,10,1);repmat(2,10,1)];

design=[group block]

 

When I check the rank (design) it`s 2 (so full rank?!). However, when I run the following

T= table(rating,categorical(group),categorical(block));

test=fitlme(T,'rating~Var2*Var3')

I get the message that my design matrix is not of full column rank. Can anyone help me out here?

[Laurie König]

I am sorry, I just realized that my above described problem does not make a lot of sense. However, I could analyze this data in a mixed anova. Could anyone help me to translate it to Linear Mixed Model?