Question: Let A and B be any matrices. (a) Prove that if both AB and BA are defined, then AB and BA are both square

Let A and B be any matrices. (a) Prove that if both

Let A and B be any matrices. (a) Prove that if both AB and BA are defined, then AB and BA are both square matrices. (b) Prove that if A has size m x n and ABA is defined, then B has size n x m. Suppose that A is a matrix satisfying ATA= A. Prove that A is then a symmetric matrix and that A = A.

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