I prefer to consider vectors as vertical and D(u, v) as the determinant of the matrix with columns u and v. Note that this does not really change the definition of D since determinants are invariant under transposition (this sounds so sciency!)

As the hint says, consider the system of equations , i.e., . Since , the system has a unique solution given by the Cramer'r rule. Find x and y, and then rewrite .