Question 8082
 It is very good  that you thought of this problem.

 Just like the definition of exponent of numbers, we define
 a^0 = 1 when the base a != 0 (nonzero).
 In other words, 0^0 is undefined. (because a^0 = a/a and a cannot be zero.)

 By the same reason A^0 is undefined when A = 0.
 In other words, A^0 = I for all nonzero square matrix.

 Forget the result from the stupid calculator. It cannot tell you the
 idea hiding inside the beautiful linear algebra.


 Kenny