write the permutation matrix(12345,35142) in cycle notation

Question

Solve the equation

Answer 1

The permutation matrix initially is the permutation of the identity matrix, which, in this case, is 5x5:

{ 0 0 1 0 0 }

{ 0 0 0 0 1 }

{ 1 0 0 0 0 }

{ 0 0 0 1 0 }

{ 0 1 0 0 0 }

35412 dictates where 1 is placed in each matrix row.

If interpreted as a cyclic permutation 1→3→1, 2→5→2, 4 maps to itself: (1 3)(2 5)(4).

Answer 2

(13)(25)(4)