Zero power of zero is not defined in mathematics. That is 0⁰ is undefined. This can be demonstrated by using a graphing calculator like TI-84. It indicated a domain error. However, the zero power of a variable, any complex or real numbers (except zero) or even a matrix is all defined. All the answers come out as unity, for matrices, the identity matrix: ⁰=1, ⁰=1, A⁰=I, where I is the identity matrix. These can all be tested using TI-84. Surprisingly, if O is the zero matrix, that is to say all its elements are zero, O⁰=I. This was tested using TI-84. Without the luxury of a PhD degree in mathematics, this remains a mathematical mystery. Why is zero power zero undefined while the zero power of the zero matrix equals the identity matrix?


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