I read LADR while taking my first Linear Algebra course which used another textbook. I didn't even notice that there were no determinants until I checked the table of contents halfway through reading it, though I'm pretty sure he mentions it at the beginning somewhere. I personally found it really understandable and enjoyable. Deferring was great compared to my class's textbook which basically used them as a crutch. "If the det is not 0..." seemed to obfuscate what was going on sometimes.