###### Definition 3.4.3

Suppose a \(2\times2\) matrix \(A\) has columns \(\vvec_1\) and \(\vvec_2\text{.}\) If the pair of vectors is positively oriented, then the *determinant* of \(A\text{,}\) denoted \(\det A\text{,}\) is the area of the parallelogram formed by \(\vvec_1\) and \(\vvec_2\text{.}\) If the pair is negatively oriented, then \(\det A\) is minus the area of the parallelogram.