For nonzero a, which statement is always true?

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Multiple Choice

For nonzero a, which statement is always true?

Explanation:
Dividing a nonzero number by itself always gives 1. This works because dividing by a is the same as multiplying by its reciprocal: a ÷ a = a × (1/a) = 1, since 1/a exists when a ≠ 0. The other statements don’t hold for every nonzero a. a × 0 equals 0, not a. So a ÷ a isn’t 0. Also, a × a equals a only when a^2 = a, which forces a to be 1 (or 0), but a is nonzero here, so it isn’t always true.

Dividing a nonzero number by itself always gives 1. This works because dividing by a is the same as multiplying by its reciprocal: a ÷ a = a × (1/a) = 1, since 1/a exists when a ≠ 0.

The other statements don’t hold for every nonzero a. a × 0 equals 0, not a. So a ÷ a isn’t 0. Also, a × a equals a only when a^2 = a, which forces a to be 1 (or 0), but a is nonzero here, so it isn’t always true.

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