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    Sets of Matrices Closed Under Matrix Multiplication

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    Please provide detailed explanation that verifies response.

    Also, please use formal set notation to prove necessity and sufficiency.

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    Solution Preview

    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 ...

    Solution Summary

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