Consider the following formula for the determinant of a 3 x 3 matrix:
det(x1y1z1//x2y2z2//x3y3z3) = x1y2z3+y1z2x3+z1x2y3 - (x3y2z1+y3z2x1+z3x2y1)
a) Show that is it linear in the first column.
b) Show that it is alternating when you switch the first and second column.
(// denotes the next row in the matrix)
I'm not sure how to prove this, any help is great. Thanks.