Combine columns of a matrix based on equality

I have a matrix of 1's and 0's and I would like to combine any column that repeats itself in the matrix - e.g if a is the matrix below I want b be the combination of any columns that are the same so b would be as shown - a new matrix with a combined repeated columns added togtehr and none repated ones left the same.

a = [1 1 1 0;1 0 0 0;0 0 0 1;1 1 1 0; 0 0 0 1]
b = [2 2 2 0; 1 0 0 0; 0 0 0 2];

The matrix I am actually dealing with is very large this is just a simplified version.

Answer 1

[Ameer Hamza]

Try this

a = [1 1 1 0;1 0 0 0;0 0 0 1;1 1 1 0; 0 0 0 1];
b = [2 2 2 0; 1 0 0 0; 0 0 0 2];

[M, ~, idx] = unique(a, 'rows', 'stable');
mul = histcounts(idx, 'BinMethod', 'integers').';
M = M.*mul;

Result

>> M
M =
     2     2     2     0
     1     0     0     0
     0     0     0     2

[Koren Murphy]

Hi Ameer - that reduces the row size but I need it to check if the columns match and if so combine the columns so the no. rows stay the same but the column size reduces??

[Koren Murphy]

Also apoliges for the confusion it was my explanation that was at error here! The true example is:

a = [1 0 1 1; 1 0 1 0; 0 1 0 1];

so b should be

b = [2 0 1;2 0 0;0 1 1]

many thanks!

[Ameer Hamza]

The logic is same. Just a little modification is needed

a = [1 0 1 1; 1 0 1 0; 0 1 0 1];
b = [2 0 1;2 0 0;0 1 1];

[M, ~, idx] = unique(a.', 'rows', 'stable');
mul = histcounts(idx, 'BinMethod', 'integers');
M = M.'.*mul;