Geometry of 2x2 Determinant

Paralellogram By Vectors

For a Parallelogram defined by vectors $a=(a_1,a_2)$, $b=(b_1,b_2)$ The area of the paralellogram is

$$\det \left[\begin{array}{cc}& \\ a_1& b_1\\ a_2& b_2\end{array}\right]$$