Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute. Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other words, provide two matrices A and B such that AB BA. But, this time, make sure your matrices A and B are not diogonal In the table below, enter your matrices A and B and verify that their products AB and BA are the same. Simplify your results as much as possible. A AB B BA Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3 diagonal matrices. Conclusion. From the results of this and previous exercises, we have found that the set D commutative under matrix multiplication because AB = BA for matrices A and B in D By contrast, note that M commutative because AB = BA for matrices A and B in M. So, while Mis not there exist subsets of M which are. And, D is just one example: can you think of others?

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