A matrix is singular iff it has____A) two eigen value. B) one eigen value. C) zero eigen value. D) none of above. 

A matrix is singular if and only if it has **zero eigenvalue**. Therefore, the correct answer is:

**C) zero eigenvalue**.

A singular matrix is one that does not have an inverse, which occurs when its determinant is zero. If a matrix has a zero eigenvalue, then its determinant is zero, making the matrix singular.

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Here are 5 related questions:
1. What is the relationship between eigenvalues and the determinant of a matrix?
2. How can you determine if a matrix is singular using its determinant?
3. What are the implications of having repeated eigenvalues for a matrix?
4. How do eigenvalues relate to the rank of a matrix?
5. Can a non-square matrix have eigenvalues?

**Tip:** The sum of the eigenvalues of a matrix is equal to the trace (the sum of the diagonal elements) of the matrix.

Explore the concept of matrix singularity and eigenvalues with a focus on determining matrix properties. Learn why a matrix is singular if it has zero eigenvalue, and grasp the connection to determinant and matrix inversion. Suitable for advanced high school students.

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