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- I need prove a property of unitary matrices, but without success.

Hi. I'm learning Quantum Calculation. There is a section about controlled operations on multiple qubits. The textbook doesn't express explicitly but I can infer the following statement:

I had hard time proving it. I only can prove that if ##V## is reversible, then ##\left (V^ \dagger V \right ) \left ( V V ^ \dagger \right )=I##.

I hope the statement is true, otherwise my inference would be wrong.

**If ##U## is a unitary matrix, and ##V^2=U##, then ## V^ \dagger V=V V ^ \dagger=I##.**I had hard time proving it. I only can prove that if ##V## is reversible, then ##\left (V^ \dagger V \right ) \left ( V V ^ \dagger \right )=I##.

I hope the statement is true, otherwise my inference would be wrong.