of all the elements
of row/column of A are multiplied by a to get a matrix B , then det(B) = a
det(A).
For a matrix ,
A = [u,v] ,
det(A) is the area of the parallelogram with sides u and v .
The following applet demonstrates this property. You can click on any two points on the panel to get arbitrary vector
Then , det[u,v] = Area(u,v) - Area(OACB) , you can change the values of a, b by
moving the sliders.