0
$\begingroup$

Show that a 2x2 scalar matrix $A$ over a field has a square root. Meaning a matrix say $B$ that satisfies $B^{2}$ = $A$.

  • 1
    Welcome to math.SE. Since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, statements phrased in the imperative ("Give", "Prove") when asking for help are considered rude by many here; please consider rewriting.2012-07-23
  • 0
    When you say "show that **a** $2\times 2$ scalar matrix" do you mean *every matrix*? or just the existence of one such matrix, e.g. $\pmatrix{4 & 0 \\ 0 & 4}?$2012-07-23
  • 0
    Hm. I think the meaning of "scalar matrix" tricked me. Perhaps OP should tell me if I misunderstood the meaning of that in my answer.2012-07-23
  • 0
    @ArturoMagidin, we do not understand your hint. In $\mathbb Q,$ both $2,-2$ fail to be squares.2012-07-23
  • 0
    @WillJagy: I was being dumb.2012-07-23

2 Answers 2