At least one eigen value of a singular matrix is A. positive B. zero C. negative D. imaginary

positive
zero
negative
imaginary

The correct answer is $\boxed{\text{B. zero}}$.

A singular matrix is a square matrix that has at least one zero eigenvalue. This means that there exists at least one nonzero vector $v$ such that $Av=0$. In other words, the matrix $A$ does not have an inverse.

The eigenvalues of a matrix are the roots of its characteristic polynomial. The characteristic polynomial of a singular matrix is a polynomial of degree at least one with at least one root equal to zero. Therefore, at least one eigenvalue of a singular matrix must be zero.

The other options are incorrect because they are not always true for singular matrices. A singular matrix can have positive, negative, or imaginary eigenvalues, but it must have at least one zero eigenvalue.

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