Discussion
Assertion (A) : A matrix is nonsingular if and only if none of its eigen values is zero.
Reason (R) : The product of the eigen values equals the determinant of a matrix.
Codes :
Answer: A
Both statements are correct and the reason explains the assertion. The determinant of a matrix equals the product of its eigenvalues, so the determinant is zero exactly when some eigenvalue is zero. A matrix is non-singular when its determinant is not zero, which means none of its eigenvalues is zero.
So (R) is the correct explanation of (A), option A.
Testing each of the remaining options against the same fact shows that every one of them fails on the point the question is asking about, which confirms the keyed answer.
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