Question

if a is a diagonal matrix, what are its eigenvalues ? a. each non zero diagonal elements are the eigen values. b . eigen values are the inverse of the diagonal elements c. all eigen values are same and equal to product of the diagonal elements d. none of the above

Answer 1

if $\bf{a}$ is diagonal matrix it means non zero elements exist only diagonal part.
e.g., $\bf{a=\left[\begin{array}{ccc}a_{11}&0&\\0&a_{22}&0\\0&0&a_{33}\end{array}\right]}$

we know, aigenvalues is found by $(A-\lambda I)=0$
where $\lambda$ is constant term.
if we do it with diagonal matrix . we get, The eigenvalues of a diagonal or triangular matrix are its diagonal elements.

hence, if a is a diagonal matrix , each non zero diagonal elements are the eigen values.

therefore option (a) is correct