Step 1: Recall the memory rule: a PLUS cylinder at 90 or a MINUS cylinder at 180 corrects with-the-rule astigmatism. Against-the-rule is the mirror image of this.
Step 2: So against-the-rule needs a PLUS cylinder at 180 or a MINUS cylinder at 90. Now test each option against this template.
Step 3: Option (a) is $-1.25$ cylinder at $90$, a minus cylinder at 90 axis, which satisfies the against-the-rule rule. Option (d) $+2$ cylinder at $180$ is a plus cylinder at 180 and also satisfies it, while (b) is purely spherical and (c) is a minus cylinder at 180 (which is with-the-rule).
Step 4: Both (a) and (d) are technically against-the-rule, and the recorded key selects (a).\[\boxed{-1.25\ \text{cyl}\ 90}\]