calculate matrix from elements of other matrix

Given matrix A = [a(i,j)], what is an efficient and (if possible) concise/readable way to calculate matrix B with elements b(i,j) = a(i,i) - a(i,j)*a(j,i) (or any other such formula)? What currently comes to mind is:

    [i, j, ~] = find(A);
    b = arrayfun(@(x,y) A(x,x) - A(x,y)*A(y,x), i, j);
    b = reshape(b, size(A));

[Walter Roberson]

duplicates http://uk.mathworks.com/matlabcentral/answers/256285-calculate-matrix-with-values-of-other-matrix