Matrix Eigen Value

Question

A 3× 3 real matrix has an eigen value i, then its other two eigen values can be
(A) 0, 1. (B) -1, i.
(C) 2i, -2i. (D) 0, -i.

Comments

Answer is $(d)$

Answer 1

correct option should be d.

because complex roots always occur in pairs. hence eigen values will be i, -i , 0.

Comments

why 0?

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@Arnabi why not B?

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because complex roots always occur in pairs. i.e if one root is a+ib another should be a-ib.

here if one root is i another should be -i.

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Ok so here it is like 0 + i and 0 - i.