He doesn't have a particular view on determinants, I got my views on determinants more from Axler than from Halmos. But Halmos' book is linear algebra as prepar

He doesn't have a particular view on determinants, I got my views on determinants more from Axler than from Halmos. But Halmos' book is linear algebra as preparation for functional analysis, so he tends not to choose a basis for proofs. I agree with you, that in practical paper computations (e.g. on exams) that determinants are an indespensible practical tool.