What pure-math reason is there for learning linear/matrix algebra?

It seems to me that it only has practical use in computer science... and frankly I dont see the power of it. Nothing can be done with matrices that cant be done elsewise... matrix algebra seems to just obfue and confuse with odd notation and weird operations. Why should I, as a pure mathematician... who appreciates anything abstract, dont get me wrong... want or need to learn to learn matrix algebra? I mean, I can do multivariate calculus in my head, solve statistics and probability problems... and here is this linear algebra cl which teaches people how to: solve simultaneous linear equations. Hello? I thought I learned that way back in algebra 2 about 15 years ago.