Problem $3($More Closure$)$

$(5$ pts$)$ Problem $1\mathrm{.}70$ in Sipser $3$rd ed$.$ page $93.$

$(5$ pts$)$ Does the following "converse closure" property hold: $"$if $A,B$ are arbitrary languages

such that $AB$ is regular, then it must be the case that $A,B$ are regular as well."? Either

prove your answer or give a counterexample.