# Sets of Matrices Closed Under Matrix Multiplication

Please provide detailed explanation that verifies response.

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

If possible, please post response as either a MS Word or PDF file.

Infinite Thanks for your time!

© BrainMass Inc. brainmass.com October 10, 2019, 3:43 am ad1c9bdddfhttps://brainmass.com/math/matrices/sets-matrices-closed-under-matrix-multiplication-432700

#### 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.

$2.19