Inequality Properties: When Does Squaring Change the Inequality?

Option A: Subtracting 1 from both sides of the inequality a<b, the inequality still holds, i.e., a-1<b-1. Hence, this option is incorrect.

Option B: Multiplying both sides of the inequality a<b by 2, the inequality still holds, i.e., 2a<2b. Hence, this option is incorrect.

Option C: Multiplying both sides of the inequality a<b by -1/3, the direction of the inequality is reversed, i.e., -a/3>-b/3. Hence, this option is incorrect.

Option D: When a=-5 and b=1, the inequality a^2<b^2 does not hold. Hence, this option is correct.

Therefore, option D is chosen.