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Let X = (S,+,*) where S is set of 3x3 matrices with integer entries,+ is matrix addition and * is matrix multiplication. Find a

Let X = (S,+,*) where S is set of 3x3 matrices with integer entries,+ is matrix addition and * is matrix 

Let X = (S,+,*) where S is set of 3x3 matrices with integer entries,+ is matrix addition and * is matrix multiplication. Find a counter example that proves that X is not a field. What is X (group, ring, ID, etc.)? List the properties studied in class it meets and properties it doesn't meet.

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