Determine if the following statements are true (always) or false. If true, give a proof. If false, give a counterexample.

(a) If the product AB is a square matrix, then the product BA is defined.
(b) If A and B are matrices of the same size, then AB is defined.
(c) If the products AB and BA are defined, then AB and BA are square matrices.

Question

27-06-2024
Mathematics

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Determine if the following statements are true (always) or false. If true, give a proof. If false, give a counterexample.

(a) If the product AB is a square matrix, then the product BA is defined.
(b) If A and B are matrices of the same size, then AB is defined.
(c) If the products AB and BA are defined, then AB and BA are square matrices.

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