("...or we be the first to throw" (Musa) said: "Nay, throw you (first)!") This means, `you magicians should go first so that we can see what magic you are going to perform and so that the true state of their affair will become obvious to the people.'
وَأَلْقِ مَا فِي يَمِينِكَ (And throw what is in your right hand - 20:69). Allah commanded Sayyidna Musa (علیہ السلام) by means of a revelation (وحی) to cast down what he held in his right hand, and when he threw down his staff it turned into a huge snake and ate up all the imaginary snakes which the Egyptian magicians had produced by their magic.
Conversion to Islam and bowing in prostration by the Pharaoh's magicians
The Egyptian magicians who were masters of their art realized at once that what they had just witnessed was not magic but a miracle brought about by a Supreme Power. Consequently they fell in prostration and declared openly their faith in Allah - the God of Sayyidna Musa (علیہ السلام) and Sayyidna Harun (علیہ السلام) . According to some traditions these magicians did not raise their heads until they had seen a glimpse of heaven and hell. (رواہ عبد بن حمید و ابن ابی حاتم وابن ال؛منذر عن عکرمہ - روح)
Tazkirul Quran
Maulana Wahiduddin Khan
The competition started with the magicians throwing their ropes and sticks on the ground where they seemed to move about in the shape of snakes. But this was an illusory effect. In other words, the ropes and sticks had not really changed into snakes. The magicians had simply created an optical illusion to play upon the imagination of the audience, so that it would temporarily appear to them as if the ropes and sticks were wriggling on the ground like snakes. Then, in accordance with God’s orders, Moses threw his stick on the ground where it immediately assumed the shape of a big snake, and started moving along the ground. At its touch, the magicians’ spell broke, then all the things which had appeared to be moving about like snakes turned back into mere ropes and sticks. The magicians had already been impressed by Moses’ speech, and now that they had had a practical demonstration of his powers, they saw with their own eyes the truth of Moses’ stand. They were now absolutely certain that the power Moses possessed was not that of human magic, but the actual ability to perform a miracle of God. This conviction was so deep that they thereupon declared their conversion to Moses’ faith.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.