Multiqubit gates

Which of the following properties for the matrix M defines unitarity?

$A):\; M=M^T, \quad B):\; M=M^\dagger, \quad C):\; M^{-1}=M^\dagger, \quad D):\; M=M^{-1}$

The answer is C).

When we write CNOT|ij>, we mean flip j if i=1. We could also redefine the gate to mean flip i if j=1. What is the matrix of this new CNOT?

The matrix representation of this new CNOT is

$\begin{pmatrix} 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0 \end{pmatrix}$

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