I was looking over my notes today, and I realized that there was a point that isn't pretty clear.(adsbygoogle = window.adsbygoogle || []).push({});

If we have the image under T (being T a matrix transformation induced by a matrix A) of the unit square, then its area should be abs(det(A)). Why is this though? I was looking at the proof and I saw that the transformation was defined as T(i) = Ti = (a c 0) and T(j) = Tj = (b d 0) [in this case i and j are the unit vectors]. However, the area of the parallelogram made between these vectors is stated to be as [[Ai x Aj]] (without the sinθ being θ the angle these vectors make). Or is it because as if they are unit vectors, they are 90 degrees to each other?

Thank you very much.

Edit: This link (around page 1) should help if i'm not clear with my explanations http://www.math.mun.ca/~mkondra/linalg2/la2set7.pdf

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# Matrix transformations and effects on the unit square

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