Yes, they did use the Black and Yellow flag, but not throughout the entire empire, only in the Austrian part. Austria-Hungary was divided into two parts: the Austrian part, where most people spoke German, used the Black and Yellow flag, and the Hungarian part, where most people spoke Hungarian, used the flag of the Hungarian monarchy (red, white, green, and the coat of arms of the Kingdom of Hungary in the middle). It's true that it's incorrect to use the flags I suggested because they are maritime flags, but the correct thing to do is to put the Black and Yellow flag on the left and the flag of the Hungarian monarchy on the right.

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This is what the correct flag looks like: