Quantum Computing: Controlled Not gate

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Analogue of XOR and Controlled-Not Gate.
Matrix representation of Controlled-Not Gate.
Prove that Controlled-Not Gate is a reversible Gate.
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Is there some reason we use [1, 0, 0, 0] rather than [0, 0, 0, 0 ]to represent |00> ?

haoliangzhang
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How do we get the matrix for cNot gate?

anirudhsrivastava