Introductory courses in Linear/Abstract Algebra

[Klungo]

At my university, the following topics are covered between Linear Algebra and Abstract Algebra.

Linear Algebra 1: Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues and inner-product spaces

Abstract Algebra 1: Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, and fields.

Under the assumption that both courses are introductory first-time proof based:

Are there any topics of abstract algebra that necessarily requires linear algebra to do?
If so, which ones and are they necessarily abstract or computational. Which would you recommend taking first if you can only pick one for the semester?

 

[genericusrnme]

Not really but linear algebra is a nice, 'easy' introduction to abstract thought because the intuitive notion of a vector as a pointer works quite well at that level.
If you're confident in your abstract thinking abilities I'd go for abstract algebra 1.