Question: Given the matrices show that A 2 = I and B 3 = I, and hence find A 1 , B 1 and (AB) 1

Given the matrices

A = [1000] 0010 0 1 0 0 0001 and B = [1 0 0 0] 0 0 1 0 0001 0 1 0 0

show that A2 = I and B3 = I, and hence find A–1, B–1 and (AB)–1.

The matrices A and B in this exercise are examples of permutation matrices. For instance, A gives

A X X X3 X4. || = [x] X3 X

and the suffices are just permuted; B has similar properties.

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