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The commutative property of multiplication states that the order of numbers in a multiplication equation does not affect the result. For example, in the equation axb=bxa, it doesn't matter if we multiply 'a' by 'b' first or 'b' by 'a' first, as the product remains the same. This property also holds true when dealing with multiple factors, as shown in the equation ax(bxc) = (axb)xc. Additionally, the multiplication of a number by -1 always results in the opposite sign, as demonstrated by the equation ax(-1) = -a. Lastly, the identity property of multiplication states that when any number is multiplied by 1, the result is always the original number itself, as in the equation ax1=a. Understanding these properties can help simplify and manipulate mathematical equations with ease.