Let \(a = -1\)
Let \(b = -2\)

Then \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |-3|= 3\)

Similarly,
Let \(a = 1\)
Let \(b = 2\)

Then, \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |3|= 3\)

Therefore either \(a,b\) can be \(-1,-2\) or \(1,2\)

The correct option should satisfy both the condition for \((a,b)\)
only option b does that since \(a*b\) is always\(+\)ve since we are multiplying \(2\) \(+\)ve numbers or 2 \(-\)ve numbers which will always be \(+\)ve.
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes