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Sets of Matrices Closed Under Matrix Multiplication

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Solution Summary

Given certain sets of 2X2 matrices, we determine the smallest sets closed under multiplication containing the original sets.

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2. Let J=[■(0&1@1&0)].
(a) What is the smallest set which contains J and which is closed under matrix multiplication?
The smallest such set is S = {I, J}. To see this, note that J2 = I, so I needs to belong to ...

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