A question about linear change of variables

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\begin{document}\noindent (ii) \textbf{(Linear change of variables)} Let $T$ be a $n \times n$ invertible matrix with real entries. Then[\int f(T(x)) |\det T| , dx = \int f(y) , dy.]\begin{document}

I'm sorry I don't know how to make the latex work, so you can watch the picture if you can not understand my word.

I only know I should use T (λn) = | det T |^(-1)λn, but I don't know how to transform left to right