Question

Which of the following example expresses the commutative law of multiplication ?

• A. $A + B = B + A$
• B. $AB = B + A$
• C. $AB = BA$
• D. $AB = A \times B$

Hint:

The word "commutative" is related to "commute," which means to travel or move around. The commutative law means the numbers can move or swap positions without changing the result.

Answer 1

The Correct Option is C

Step 1: Define the commutative law of multiplication. The commutative law states that when two numbers are multiplied, their order can be changed without affecting the product. In algebraic terms, \(a \times b = b \times a\).
Step 2: Analyze the given options.

(A) A + B = B + A: This expresses the commutative law of \textit{addition}.
(B) AB = B + A: This is not a standard mathematical law.
(C) AB = BA: This perfectly represents the commutative law of multiplication, where the order of factors A and B is swapped.
(D) AB = A B: This just shows two different notations for multiplication; it doesn't illustrate a law.
Thus, AB = BA is the correct expression of the commutative law of multiplication.