Area of triangle as a determinant I am having a hard time with the following question
Let $P_0,P_1,P_2$ be points in $\mathbb{R}^2$. We denote $r_i = P_0P_i, i =1,2$. Let P be the 2 by 2 matrix with rows $r_1$ and $r_2$. Let A denote the area of the triangle with vertices $P_0,P_1,P_2$. Explain why $A=\frac{1}{2}|\det(P)|$
Any hints or tips would be greatly appreciated.

There's a small error in notation: the rows are made up of the coordinates of the vectors $\vec{P_0P_i}$.
Hint: it is a basic result on determinants that the absolute value of this determinant is the area of the parallelogram built on these vectors.
