Let (e1,...,en) be a north on ormal basis for E. If X and Y are arbitrary n×n matrices, denoting as usual the jth column of X by Xj, and similarly for Y, show that  Use this to prove that      iff the...

Let (e1,...,en) be a north on ormal basis for E. If X and Y are arbitrary n×n matrices, denoting as usual the jth column of X by Xj, and similarly for Y, show that
 Use this to prove that
  iff the column vectors (A1,...,An) for man ortho nor mal basis. Show that the conditions AA=In,AA=In, and A−1=Aar equivalent.