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Lit., "know" - but since this expression denotes here remembrance rather than knowledge in the proper sense of the word, it can be suitably translated as above.
I.e., "enables me to win back my brother Benjamin".
Kabir may mean the eldest. But in xii. 78 above, Kabir is distinguished from Shaikh, and I have translated the one as "venerable" and the other as "aged". In xx. 71 Kabir obviously means "leader" or "chief", and has no reference to age. I therefore translate here by the word "leader", that brother among them who took the most active part in these transactions. His name is not given in the Qur-an. The eldest brother was Reuben. But according to the biblical story the brother who had taken the most active part in this transaction was Judah, one of the elder brothers, being the fourth son, after Reuben, Simeon, and Levi, and of the same mother as these. It was Judah who stood surety to Jacob for Benjamin (Gen. xliii. 9). It is therefore natural that Judah should, as here, offer to stay behind.
The pledge he had given was to his father, and in Allah's name. Therefore he was bound both to his father, and to Allah. He must await his father's orders and remain here as pledged, unless Allah opened out some other way. For example the Egyptian Wazir might relent; if so, he could go back with Benjamin to his father, and his pledge would be satisfied.