SOLUTION: 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 iden

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
RELATED QUESTIONS
I have not really been to good at math and I never had a good Alg. teacher b/c they all... (answered by longjonsilver,richwmiller)

Is there a way to explain the Quadratic Formula in laymans terms??? I am going to teach... (answered by ichudov)

The diagram below, not drawn to scale, EFGH is a rectangle. The point D on HG is such... (answered by Alan3354)

To express 20 as a sum of different powers of 2, we would write 20 = 24 + 22. The sum of... (answered by jsmallt9)

a square matrix A is said to be idempotent A^2=A (a)give an example of idempotent... (answered by Edwin McCravy)

Hello! My name is Nevan and I am currently in Alg 2. I have this assignment due in a few... (answered by rothauserc)

Hi-I'm having troubles with a problem that is based on Mathematica. This problem deals... (answered by venugopalramana)

The symmetrix positive definite matrix A = {{{(matrix ( 3, 3, 16, -8, -4, -8, 29, 12, (answered by ikleyn)

My daughter has a pre-algebra problem she nor I can figure out how to answer. The math... (answered by Fombitz,MathTherapy)