There are six 3 by 3 permutation matrices P What numbers can

There are six 3 by 3 permutation matrices P. What numbers can be the determinants of P? What numbers can be pivots? What numbers can be the trace of P? What four numbers can be eigenvalues of P?

Solution

Determinants possible are only 0,1

Pivot possible are 1 and -1

Trace possible values are - 0,1,2,3

Eigen Values are - 1,-1,2,3,