Algebra and convex geometry for proving uniqueness of John ellipsoids

Question

I am looking at the proof about the uniqueness of John ellipsoids. The book I am looking at starts by supposing that there are two different ellipsoids $\epsilon:=S(\mathbb{B}_2^n)+x$ and $\epsilon^{'}:=S^{'}(\mathbb{B}_2 ^n)+x^{'}$ contained in a convex body $K$, both are John ellipsoids, where $S$ and $S^{'}$ are positive definite matrices. Now the book says, by linear invariance we may assume that $S=I$ identity matrix. What does it mean by linear invariance? can you help me out? Thanks