Brian Schott wrote:
> And finding
> the inverse by reversing each cycle (below) is also new to
> me.

This is actually easy to see.  The cycle 2 0 1 means 2->0, 0->1, 1->2. 
Reversing the cycle reverses all arrows. If a permutation is expressed as
a product of disjoint cycles, you can apply this process to each in any
order.

Best wishes,

John


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