Question About Basic Rules of Elementary Algebra

logic linear-algebra algebra-precalculus elementary-set-theory systems-of-equations

Multiplying both sides of an equation by a nonzero number is reversible (invertible), and so information is preserved (i.e., the solution of the multiplied equation is the same as the solution of the original equation).

On the other hand, multiplying both sides by $0$ is not reversible, and so information is lost.

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