Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) Matrix multiplication is commutative.(b) If the matrices A, B, and C satisfy AB = AC, then B = C.(c) The transpose of the sum of two matrices equals the sum of their transposes.

Question

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) Matrix multiplication is commutative.
(b) If the matrices A, B, and C satisfy AB = AC, then B = C.
(c) The transpose of the sum of two matrices equals the sum of their transposes.

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