Why, when Yosef swore that they would not leave Egypt (or his palace) unless their younger brother came to Egypt, did he swear by the life of Pharaoh?
Rashi: Because he was swearing falsely. 1 He first told them that they would all be incarcerated except for one, and then he allowed all but one of them to leave Egypt. 2
A Shevu'ah that mentions no name is automatically in the name of Hashem. If one attributes the Shevu'ah to anything else, it is Batel. However, it disgraces the king if one swears in his life and does not keep his word (Rosh Hashanah 17b - PF).
The same applies in the next verse, "Chei Pharaoh, Ki Meraglim Atem" (42:16), even though he knew that they were not. Hadar Zekenim (to 42:3) - When he swore falsely, he swore by the life of Pharaoh, for he hated Pharaoh's life. (Why didn't Yosef appreciate the good that Pharaoh did for him? Pharaoh deified himself (refer to 41:1:4:2 and the note there), which is an awesome brazenness to Hashem. It was Hashem Who caused Pharaoh to crown Yosef! - PF)
What exactly, would their younger brother's arrival prove? They could bring a stranger!
Seforno: If they were not brothers, a stranger would never agree to accompany them and to lie, thereby risking his life (together with theirs). 1
Bechor Shor: Yosef asked for a description of the younger brother, lest they bring someone else. 2
Moshav Zekenim #1: He did not suspect them to do so. 3
Moshav Zekenim #2: They did not resemble anyone else, only each other.
Ohr ha'Chayim #1: Really, it will not prove that you entered [different gates] in order to find and redeem Yosef. Even so, I will accept this (as proof that you are not spies).
Ohr ha'Chayim #2: If he comes, I will believe that you intended to free Yosef through appeasing the buyer. 4 (Yosef hid his real intent from them. 5 )
Malbim (to 42:16): Yosef said that they will send a messenger from Egypt with a letter from them telling their brother to come. They will be incarcerated and unable to talk with their brother, and Yosef can interrogate them separately.
Oznayim la'Torah (to 42:16): If they substantiated their claim that they had a brother by bringing him down, Yosef would believe that they volunteered the information before being asked because that was their nature. But if they did not, it would prove that they were lying and were spies, who volunteered the information in order to put him off the scent in the way that spies do.
A son of the 10 'Meraglim' might agree, especially Shimon's, in order to free his father. However, if the 10 were not truly brothers, he would be afraid, lest Yosef ask him questions about the family that a stranger would not know! (PF)
Seemingly, they could conspire to describe a neighbor, or one of their sons. Perhaps Yosef asked them not in front of each other, before he demanded to see Binyamin, so they had no chance to do so. Or, they would fear lest the translator hear them conspire! (PF)
Refer to 42:15:2:1. Alternatively, they would fear lest he know through Nichush that it is not their brother. Yosef showed great knowledge about them, and attributed it to Nichush (refer to 42:14:1:1*; see Rashi to 43:7. - PF)
Ohr Yakar: Even though they admitted that they would kill to take him, if needed (refer to 42:14:1:1), Yosef claimed that they had no intend to redeem, only to take by force. (He could ask to see if they brought much more money than needed to buy as much grain as their donkeys can carry! However, extra money is not a proof. Perhaps they were concerned lest the price rise greatly, due to the great famine, or intended to buy other matters as well, or they stole it from others! - PF)
Ohr Yakar; I.e. to fulfill the first dream.
Why did Yosef demand that Binyamin come? He knew that this would pain his father!
Moshav Zekenim: Yosef wanted only that his father come to Egypt due to Binyamin, and he will know that his father is alive. He reasoned that if he tells them now that he rules over Egypt, amidst hatred they will not tell Yaakov.
Ramban: He needed to fulfill the dreams. Refer to 42:9:4:1**.
Why did Yosef say "b'Zos Tibachenu"?
Malbim: If something leans more to the side of guilt (e.g. that you are spies), one needs a stronger proof of innocence than if leans more to the side of innocence.
QUESTIONS ON RASHI
Rashi writes: "'Chei' Pharaoh - If Pharaoh shall live." What is Rashi telling us?
Gur Aryeh: Do not translate literally, to mean 'The life of Pharaoh [is only] if you [do] leave this place!" Rather, this is an oath by the life of Pharaoh, that they would not leave unless they fulfilled his condition.
Rashi writes: "Mi'Zeh - from this place." How else might I have understood this?
Gur Aryeh: We might have translated, '... if you leave this predicament (of suspicion) you now find yourselves in.' Rather, Rashi tells us that "leaving" is always in terms of a place.