This is an exercise from Tu's book on manifolds, which I am self-studying from. It is a rather simple computational problem, but I wanted to verify my solution first before proceeding with the book. The problem asks for $f, g \in A_2(V)$, to compute $f \wedge g$.
My solution is $$\begin{align}(f \wedge g)(v_1, v_2, v_3, v_4) = &f(v_1, v_2)g(v_3,v_4) - f(v_1, v_3)g(v_2, v_4) \\+ &f(v_2, v_3)g(v_1, v_4) - f(v_2, v_4)g(v_1, v_3) \\+ &f(v_3, v_4)g(v_1, v_2)+ f(v_1,v_4)g(v_2, v_3).\end{align}$$
I know yes and no questions are frowned upon here, so I apologize in advance, but I would like to ask if this solution is correct.