This is a great book with wonderful ideas and organization. The proofs are well developed, original, and intuitive and the book provides a really nice foundation to Vector spaces, Matrices, Determinants, followed by an intro to probability theory and then a deep dive.
I could not bring myself to rate this higher than 3 however because I found it frustrating that on every page there would be three or four theorems where the proof is omitted because they were "obvious". In every case they were indeed obvious; after you spent three days thinking about it! A little hint of a direction would have made this book much more accessible.
Additionally, some of the wording was careless. For example, given a matrix A he starts using the notation M(A) (manifold of A) without any definition. Then about 10 pages later he defines it as the Manifold of the column vectors of A. Or little inconsistencies in the type for example he refers to "an mxn matrix" but then a few lines later "a nxm matrix." Which is it, "a" or "an"?
If you glide freely through the worlds of mathematics you will thoroughly enjoy this book. For me, graduate school is a fading memory and so I will fall back on something a little more basic, before I try again on Rao.