Find the determinant of a transformation matrix given two sets of 3 vertices

determinantlinear algebralinear-transformationsmatrices

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I'm not sure how to use this information. It also isn't clear, I'm assuming the points are in their respective orders. If so, then I know:

$
\begin{bmatrix}
1\\
0\\
\end{bmatrix}
\quad
$
multiplied by unknown transformation matrix = $
\begin{bmatrix}
0\\
6\\
\end{bmatrix}
\quad
$

How would I know what it was though? Apparently the answer is that the determinant of matrix $A$ is $15$, but I'm not exactly sure how they got that answer.

Any ideas? Thanks.

Best Answer

Hint. You don't need to find $A$ to know its determinant. All you have to know is that the determinant is the factor by which $A$ scales all areas.

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