GMAT Problem Solving (PS) | Re: If n denotes a number to the left of 0 on the number line

Math mods and others - Please check my approach:

Given: n is less than 0, implying n is negative.

Also given:\(n^2\) <\(\frac{1}{100}\)

Square rooting both sides:

n< -\(\frac{1}{10}\) AND n <\(\frac{1}{10}\)

Reciprocating both the inequalities,
\(\frac{1}{n}\) <-10 AND \(\frac{1}{n}\) <10

Since,\(\frac{1}{n}\) MUST be less than -10 and 10 at all times, the option that always satisfies this is A.

Is this a right approach? I always falter when removing the squares on both sides of the equation/inequality and I want to make sure my approach is
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