Commentary for Genesis 42:20

ויאמנו דבריכם— means so shall your words be verified and confirmed. Other examples are, (Numbers 5:22) “It is true, it is true (אמן אמן)”, and (1 Kings 8:26) “Let thy word, I pray thee, be verified (יאמן).”

ולא תמותו, he meant that they would not die here, as he was able to have them killed also in the land of Canaan if they would not come back of their own free will.

ויאמנו דבריכם. "And your words will be verified." This means that if the brothers did not agree it would prove their guilt and that that was the reason they did not dare leave one brother behind. Moreover, it would be forbidden to hand over an unnamed individual if there was a likelihood he was guilty of the death penalty. Another possible meaning of these words is simply that by bringing Benjamin down to Egypt Joseph would make sure their families would not die of starvation. The brothers referred to this when they told their father in verse 34 that Joseph had offered ואת הארץ תסחרו, "you may travel freely in the land."