How does current equal \$i_o\$ in this op amp problem?
It's just a case of asking yourself what current flows into the input of an ideal op-amp then seeing what remains to flow in the resistors: -

The trouble is that it looks like the set answer is wrong because the current into the 1 kΩ resistor is upwards and not downwards. So, the right answer should be \$-i_0\$ as I see it.