If is a complex vector space and is a normal operator with only one distinct eigenvalue, then which of the following is true?

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If<br><img src='https://www.fatskills.com/images2/GradExams/46966CA9-BBE0-4719-A5E2-76FC70B11887.png' height='15' width='14'/> is a complex vector space and<br><img src='https://www.fatskills.com/images2/GradExams/38409966-4AFF-447C-8374-D83A9632557A.png' height='14' width='14'/> is a normal operator with only one distinct eigenvalue<br><img src='https://www.fatskills.com/images2/GradExams/84A7CFBB-0E75-4560-AC09-C60B3C81FB96.png' height='15' width='10'/>, then which of the following is true?