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Study the following assertions about a square matrix

(i) The sum of the eigen values of A is equal to its trace

(ii) The product of the eigen values of A is equal to its determinant

(iii) All eigen values of A are non-zero, if and only if A is non-singular

(iv) If A^{-1}exists, then the eigen-values of A^{-1}are equal to the reciprocal of the eigen

Which of the following is correct with respect to above assertions?### Options :-

- Only (iii) and (iv) are true
- Only (i) and (ii) are true
- Only (ii), (iii) and (iv) are true
- (i), (ii), (iii), (iv) all are true

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