How to get all the columns in model.matrix

Question

Suppose we have a data.frame :

> df <- data.frame(A = c('a','a','b','c','c','b','a'), B = c('d','e','e','e','f','f','g'))

On printing the values we'll get:

> df
  A B
1 a d
2 a e
3 b e
4 c e
5 c f
6 b f
7 a g

On applying model.matrix , it gives:

> d <- model.matrix(~.,df)
> d
  (Intercept) Ab Ac Be Bf Bg
1           1  0  0  0  0  0
2           1  0  0  1  0  0
3           1  1  0  1  0  0
4           1  0  1  1  0  0
5           1  0  1  0  1  0
6           1  1  0  0  1  0
7           1  0  0  0  0  1

Now, as we could see in the factor df$A, there are 3 unique characters i.e ( a, b, c). But, in its equivalent model.matrix we have Ab, Ac. Similarly, in case of df$B, Bd is missing.

So, My question is how can we get all the columns in a model.matrix representation, if i'm neglecting the Intercept ?