Question

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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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