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Question: let a be the set of 2 2 boolean...

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Let A be the set of 2 × 2 Boolean matrices. Given matrices M and N in A, we define the order relation ≤ as M ≤ N if and only if mij ≤ nij, for all 1 ≤ i ≤ 2, 1 ≤ j ≤ 2. Prove that (A, ≤) is a Boolean algebra by showing an appropriate isomorphism. (Hint: you do not need to write all the matrices in set A).

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