Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A is an m xn matrix and B is apxq matrix. Because AB is defined, you have that --Select- v and so AB is an --Select-- v square matrix. Select--- v and AB is a(n) Select--- matrix. Because BA is defined, you have that Likewise, because BA is defined, -Select-- v and BA is a(n) ---Select-- v matrix. Because AB is defined, you have -Select-- v Therefore, BA is an -Select---- v square matrix.

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