function P = mat_prod(A,B)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% mat_prod - matrix multiplication
%
% Inputs
% 
% A, B  - matrices to be multiplied
%
% Output:
%
% P - resulting product
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[a1,a2] = size(A);
[b1,b2] = size(B);

if ~(a2 == b1), error('A and B must have the same inner dimensions'); end

P = zeros([a1 b2]);

for i = 1:a1
    for j = 1:b2
        for k = 1:a2
            P(i,j) = P(i,j) + A(i,k)*B(k,j);
        end
    end
end