matrix exponential: M^0

Dear All, 

I would like to ask why the zeroeth power of a matrix gives me a matrix
of ones rather than the identity matrix:

Because ^0 gives you the zero-th power of the _elements_ of the 
matrix, not the matrix itself. A matrix of 0^0 is all 1s.

  Similary, '*' multiplies the elements together, it doesn't do matrix 
multiplication. For that you need %*%.

  There is no %^% operator for matrix exponentials.

Baz