Question 8082: My text(Anton Elem. L.Alg 8th ed) states on pg. 44 "If A is a square matrix, then we define the nonnegative powers of A to be... A^0 = I" So a matrix to the zeero power is the identity matrix. Is this true for ALL matricies, including a zero matrix.
i.e. is [0]^0=[1]? My Ti-92 says it it is, but 0^0 is not 1. Why?
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! 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
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