  For a q by q matrix x=(x_{i,j}) we let J(x)=(x_{i,j}^{-1}) be the Hadamard
inverse, which takes the reciprocal of the elements of x . We let
I(x)=(x_{i,j})^{-1} denote the matrix inverse, and we define K=I\circ J to be
the birational map obtained from the composition of these two involutions. We
consider the iterates K^n=K\circ...\circ K and determine degree complexity of
K, which is the exponential rate of degree growth of the degrees of the
iterates.
