An algebra problem by rounak chatterjee

Algebra Level pending

let I denote a 3x3 identity matrix and p is obtained by rearranging the columns of I

WHICH OF THE FOLLOWING IS CORRECT?

  1. there are six distinct choices of P and determinant of P is 1
  2. there are six distinct choices of P and determinant of P is - 1 or +1
  3. there are more then one choices for P and inverse of P is always equal to I
  4. there are more then one choices for P and some of them are invertible
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