Why is the Dollar Index strong after the Fed dropped the Fed Fund Rate?

It is always very hard to precisely identify the causes of a particular index variation. Here, note that the U.S. Dollar Index (DXY) is a measure of the value of the US dollar relative to a basket of foreign currencies. So, the DXY Index goes up when the U.S. dollar gains value when compared to other currencies. Given that the economic slowdown is global, the US dollar could strengthen relative to other currencies

Because of forced selling and a scramble for cash. People responding to margin calls, having to repay bonds etc etc. Cash demand went through the roof.

While the fed has dropped interest rates, so have almost all other countries. The US Dollar Index (DXY) is a measure of the value of the US dollar relative to a basket of foreign currencies, so if all countries drop interest rates, the relative change should be zero.

In economically troubled times, a lot of companies and people flock to the US to buy US dollars, because it is considered a safe currency. As most trade is done in US dollars this is also the most stable currency relative to commodity prices.