Textbooks in which determinant is defined as an alternating multilinear map

I'm interested in this abstract definition of determinant, i.e. determinant is defined as an alternating multilinear map. Could you please suggest me some Linear Algebra textbooks that define determinant in such way.

Thank you so much for your references!

Solution 1:

Linear Algebra by Hoffman and Kunze does determinant theory in the way you mentioned. Further it treats matrices not just over fields but over arbitrary commutative rings with unity.

Solution 2:

That's how it's done in my favorite Linear Algebra textbook: Katsumi Nomizu's Fundamentals of Linear Algebra. See its sixth chapter.