Matrix form of trivector triple product

Question

If $a \wedge b = a \otimes b - b \otimes a$ then what is $a \wedge b \wedge c$

I know it's supposed to be a trivector but what is it in Matrix form?

Answer 1

$e_1 \wedge e_2 \wedge e_3$ = $ \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0 \\ \end{bmatrix}$ $ \begin{bmatrix} 0 & 0 & -1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ \end{bmatrix}$ $ \begin{bmatrix} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}$

$ a \wedge b \wedge c = a \otimes b \otimes c - a \otimes c \otimes b + c \otimes a \otimes b - c \otimes b \otimes a + b \otimes c \otimes a - b \otimes a \otimes c$