You can do this in one line using the functions NUM2CELL to break the matrix X into a cell array and CELLFUN to operate across the cells:

Use with AIZ = cellfun(@(x) x*Y,num2cell(X,[1 2]),'UniformOutput',false);

The result Z is a 1-by-C cell array where each cell contains an A-by-D matrix. If you want Z to be an A-by-D-by-C matrix, you can use the CAT function:

Use with AIZ = cat(3,Z{:});

NOTE: My old solution used MAT2CELL instead of NUM2CELL, which wasn't as succinct:

Use with AI[A,B,C] = size(X);
Z = cellfun(@(x) x*Y,mat2cell(X,A,B,ones(1,C)),'UniformOutput',false);