Appendices - Section A.1 - Real Numbers and the Real Line - Exercises A.1 - Page AP-6: 25

Proof given below.

Work Step by Step

We alternatively defined $|x|$ as $|x|=\sqrt{x^{2}}$ Apply on $x=ab:$ $|ab|=\sqrt{(ab)^{2}}=\sqrt{a^{2}b^{2}}=\sqrt{a^{2}}\cdot\sqrt{b^{2}}=|a|\cdot|b|$

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