Explanation Consider the statement, “The product A B and B A are defined if and only if A and B are square matrices of same order”. Let A = [ 2 0 − 3 − 4 1 − 1 ] 2 × 3 and B = [ − 1 2 5 6 1 − 1 ] 3 × 2 Therefore, by definition of matrix multiplication, As the number of columns in A is equal to the number of rows in B , then the product A B is defined. Therefore, A B has dimension 2 × 2 . A B = [ 2 0 − 3 − 4 1 − 1 ] [ − 1 2 5 6 1 − 1 ] By using definition of matrix multiplication, = [ ( 2 ) ( − 1 ) + ( 0 ) ( 5 ) + ( − 3 ) ( 1 ) ( 2 ) ( 2 ) + ( 0 ) ( 6 ) + ( − 3 ) ( − 1 ) ( − 4 ) ( − 1 ) + ( 1 ) ( 5 ) + ( − 1 ) ( 1 ) ( − 4 ) ( 2 ) + ( 1 ) ( 6 ) + ( − 1 ) ( − 1 ) ] = [ − 2 + 0 − 3 4 + 0 + 3 4 + 5 − 1 − 8 + 6 + 1 ] = [ − 5 7 8 − 1 ] 2 × 2 Similarly, as the number of columns in B is equal to the number of rows in A , then the product B A is defined

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Chapter 1.6, Problem 9TFE

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Whether the statement, “The product AB and BA are defined if and only if A and B are square matrices of same order” is true or false.

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Chapter 1.6, Problem 8TFE

Chapter 1.6, Problem 10TFE

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Whether the statement, “The product A B and B A are defined if and only if A and B are square matrices of same order” is true or false.

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Whether the statement, “The product AB and BA are defined if and only if A and B are square matrices of same order” is true or false.

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