There is a great book published in Russian "ЗАДАЧИ И ТЕОРЕМЫ ЛИНЕЙНОЙ АЛГЕБРЫ" (Problems and theorems in linear algebra), by Victor V. Prasolov. English translation was done by American Mathematical Society. Unfortunately, this translation is for the first edition of the book. Latest edition is available for free: http://prasolov.loegria.net/linalg.pdf (hint is you want to print it out, Amazon printing service is gre…
It's a great book, though for a completely different audience than Strang. It collects hundreds of apocryphal results from 400 years of linear algebra, most with proofs, some fairly deep.
Here's the English 1st edition: https://staff.math.su.se/mleites/books/prasolov-1994-problem...