Could someone explain all parts on how to solve this question and please explain

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Could someone explain all parts on how to solve this question and please explain it in as much detail as possible and do all the parts 1-3 of the questions. This is Linear alegebra

74. Guided Proof Prove that if the product AB is a square matrix, then the product BA is defined Getting Started: To prove that the product BA is defined, you need to show that the number of columns of B equals the number of rows of A (i) Begin your proof by noting that the number of columns of A equals the number of rows of B. (ii) Then assume that A has size m x n and B has size n X p. (iii) Use the hypothesis that the product AB is a Square matrix.

Explanation / Answer

Let A be a matrix of order mxn and B be a matrix of order nxp.

Then the order of the product AB by definition is mxp.

Given AB is a square matrix, hence m must be equal to p.

So A has order mxn and B has order nxm.

Thus the product BA is clearly defined.(No of rows of A=No of columns of B = m)

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