How do I show below is 1-1. I also know the natural basis is $R^2$enter image description here

enter image description here

  • $\begingroup$ What have you tried? $\endgroup$
    – Krup'a
    Jan 18 '20 at 20:46
  • $\begingroup$ I’m not sure where to even start. I think I’d need to change $R^2$ into a 2x2 matrix though $\endgroup$
    – Ellie
    Jan 18 '20 at 20:48
  • $\begingroup$ Why do you want to calculate $R^2$? (I'm assuming you mean $R=R_{\pi/3}$) The question is about $R$, isn't it? $\endgroup$
    – Krup'a
    Jan 18 '20 at 20:52
  • $\begingroup$ You need to show the invertibility of $R_{\pi/3}$. The easiest way would be to calculate the determinant of $R_{\pi/3}$. $\endgroup$
    – Krup'a
    Jan 18 '20 at 20:54
  • $\begingroup$ Show that the determinant is not zero. $\endgroup$ Jan 18 '20 at 20:54

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