how to multiply matrix vectors with one column?

if i have matrix M = [1 0 1 0; 1 0 0 1;1 1 1 0;1 1 1 1; ...] and i want to multiply each row with one cloumn B=[1 0 0 1] how to do this?

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M*B'

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If i want to multiply this answer(say its C) with the same matrix M (C1=C*M), then multiply the new answer (say its C1) with M (C2=C1*M) and so on for many times until one answer is repeated.then the code stop and save the results in a form of matrix. how to do this?
B' is 4x1 M is 4x4 then C=M*B' would be also 4x1. then you can not compute C*M since C is 4x1 and M is 4x4.
But you can compute C1=M*C and then C2=M*C1. Exactly as we are writing this.
that what i meant....C1=M*C and then C2=M*C1. and so on until one answer is repeated. i try to use for loop but it didn't work

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