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    Question

    ​​

    A.

    The eigenspace of A  for the eigen value zero is 2-dimensional .

    B.

    All the eigen-values of A are real .

    C.

    ​​​

    D.

    A is diagonalizable.

    Correct option is B

    Result : The complex eigen values of any matrix always exist in conjugate pairs .

    Now, as T2T^2  divides characteristic polynomial of A ,

    as order of matrix is 3 then only one eigen value remains which must be real, because complex eigen values of any matrix always exist in conjugate pairs .

    there cannot be only one  complex eigenvalue .

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