Given, the adjoint of is defined to be the operator, such that which is true?

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Given<br><img src='https://www.fatskills.com/images2/GradExams/9EDFE78D-3C4D-4DE6-B431-1FF9AC8560BF.png' height='20' width='81'/>, the adjoint of<br><img src='https://www.fatskills.com/images2/GradExams/38409966-4AFF-447C-8374-D83A9632557A.png' height='14' width='14'/> is defined to be the operator<br><img src='https://www.fatskills.com/images2/GradExams/E969117F-1FE0-4DD9-B4A9-E847F018D8B0.png' height='20' width='89'/>, such that which is true?