@TechTV it do be a comment from 6 years ago I now have a bachelor of computing and software systems, minoring in mathematics that being said, it's good for closure if somebody else is curious so perhaps a more involved answer: (though there is probably a simpler answer) if we represent scaling as a linear transformation `f` on a real valued inner product space of dimension `n` (such as 3D euclidean space), then we can represent this transformation by a `n x n` matrix `[f]`, so it will have the form `P D P^-1` once diagonalised over the reals (it can be since it only does scaling) where the diagonal terms of `D` are the eigenvalues of `f`, for example with 3 dimensions `D` is of the form `[a 0 0; 0 b 0; 0 0 c]`. then the volume in the space (the n-dimensional measure) will be scaled by the determinant of `[f]` (because the inner product is bilinear and associative), which is `|[f]| = |P||D||P^-1|`, now `|P| = 1/|P^-1|` so `|[f]| = |[D]|` , and for a row echelon form matrix (which a diagonal matrix is) is just the product of the diagonal terms, so `|[f]| = a * b * c * ...`, so if all the eigenvalues are the same (`a = b = c = ...`) the scaling of the volume is `a^n` (so `a^3` in the 3 dimensional case, `a^2` in the 2 dimensional case)
