Split matrix into multiple matrices with same value

Let's say I have a matrix as with the following values:

A = [1 10
     2 10
     3 10
     4 10
     20 1
     20 2
     20 3
     20 4];

then I would like to split this into two separate matrices:

B = [1 10
     2 10
     3 10
     4 10];
C = [20 1
   20 2
   20 3
   20 4];

A is just an example, there could be multiple occasions of the same x or y value. So after C is done there could be more values where either the x or the y value is the same. I want all occasions of same values, either x or y, to be split into a new matrix/new dimension of an existing matrix. Can this be done preferably without a loop? It doesn't really matter that much if it's in a loop though.

[Jan]

What happens for:

A = [1, 2; ...
     1, 3; ...
     2, 3, ...
     2, 4]

?