A common notation for a permutation n of the integers {1..........m) is as a 2 × m matrix

indicating that n takes i to n(i).
(a) Show that such a permutation corresponds to the permutation matrix with 1's in positions (Ï€(j), j) for j = 1..........m.
(b) Write down the permutation matrices corresponding to the following permutations:
(i)

(ii)

(iii)

(iv)

Which are elementary matrices?
(c) Write down, using the preceding notation, the permutations corresponding to the following permutation matrices:
(i)

(ii)

(iii)

(iv)

123.m 3 2 2 1 3 2 4 1 2 4 2 2 4 5 100 001 0-0 0100 1000 0001 00-0 0010 0100 1000 0001 000-0 10000 00-00 00001 01000