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Given that A is an n × n matrix and I is the n × n identity matrix, select all the correct responses below.

A Every diagonalisable matrix is normal.

B If A is Hermitian, then [tex]A^TA[/tex] is also Hermitian.

C If all eigenvalues of A have algebraic multiplicity 1, then it is diagonalisable.

D If A is Hermitian, then A + I is always invertible.

E If B = A*A, then B is Hermitian.

F None of the above

I know that A is wrong because it is only every unitarily diagonalisable matrix that is normal. I think B is correct because if it is Hermitian it means that A is equal to the complex conjugate of the transpose. So really A is a symmetric matrix and [tex]A^T=A=A^*[/tex]. Not too sure about C in the end. I think D is wrong because the Hermitian matrix doesn't have to be invertible to begin with. E is also wrong because you don't know enough information about the matrix B to make that statement. Obviously the selection then can't be "none of the above".

I think I might have them right, but I would like to check. ALthough I don't actually know about C so if someone could explain that to me I'd be grateful.

Thanks