Use linear algebra to show that X = 1, where X is the single-Chit NOT operator. Let Cij be the controlled not (CNOT) operator on a system of N Cbits. The action of this operator is to flip the state of bit j (the target bit) only if the bit i (the control bit) is 1. Otherwise, leave bit j alone. In any case, bit i remains unchanged. Specifically, let N = 3: (a) Write the result of a Co2 operation on each of the eight input states, b2b, bo). (b) Write the matrix representation for Co2. (c) Use linear algebra to determine whether Co2 is a unitary operation. Feel free to use MATLAB to calculate the result and avoid human error. Use linear algebra to show that X = 1, where X is the single-Chit NOT operator. Let Cij be the controlled not (CNOT) operator on a system of N Cbits. The action of this operator is to flip the state of bit j (the target bit) only if the bit i (the control bit) is 1. Otherwise, leave bit j alone. In any case, bit i remains unchanged. Specifically, let N = 3: (a) Write the result of a Co2 operation on each of the eight input states, b2b, bo). (b) Write the matrix representation for Co2. (c) Use linear algebra to determine whether Co2 is a unitary operation. Feel free to use MATLAB to calculate the result and avoid human error