Find the area of the parallelogram formed by the vectors (1, 1), (1, 3).

Question

I believe the answer is 2.

the second part is the part I can't figure out.

Suppose we transform the plane (with the parallelogram in it) by multiplying by a matrix A where det(A) = 5. Compute the area of the transformed parallelogram.

Is it just 10?

Answer 1

$$A=|{\bf a}\times {\bf b}|= \begin{vmatrix} i&j&k\\ 1&1&0\\ 1&3&0 \end{vmatrix}=|2 k|=2. $$

The second answer is also coorect as $\det(AB)=\det(A)\det(B)$.