I would definitely choose Strang to begin learning Linear Algebra. He develops the geometric intuition you need for applying it in other subjects such as Calcu

I would definitely choose Strang to begin learning Linear Algebra. He develops the geometric intuition you need for applying it in other subjects such as Calculus or Statistics or Physics. Linear Algebra is not just Abstract Algebra, at least for most of us, including most mathematicians. After Strang, or even alongside him, if you want more rigour then you would benefit from a text like that of Anton, or Friedberg, or Curtis or, God forbid, Axler. FYI I bought Axler's book (3rd edition).