Prove the following statements. a.) If A and B are square and invertible, then (AB) =BA....

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Prove the following statements. a.) If A and B are square and invertible, then (AB) =B¹A¹. b.) If c is a scalar and A, B, and C are of the appropriate sizes, then A(B+C) = AB+ AC. (Prove it using a Left Hand Side/Right Hand Side argument.) c.) If A is a square matrix, then A+ A¹ is symmetric. d.) If A and B are square matrices such that B and AB are invertible, then A is nonsingular. Prove the following statements. a.) If A and B are square and invertible, then (AB) =B¹A¹. b.) If c is a scalar and A, B, and C are of the appropriate sizes, then A(B+C) = AB+ AC. (Prove it using a Left Hand Side/Right Hand Side argument.) c.) If A is a square matrix, then A+ A¹ is symmetric. d.) If A and B are square matrices such that B and AB are invertible, then A is nonsingular.