If q is a characteristic root of an singular matrix A, then prove that `(|A|)/(q)` is a characteristic root of a adj A.

If alpha is a characteristic root of a nonsin-gular matrix, then prove that |A|/alpha is a characteristic root of adj A.

If alpha is a characteristic root of a nonsin-gular matrix, then prove that |A|/alpha is a characteristic root of adj A.

If alpha is a characteristic root of a nonsin-gular matrix,then prove that |A| alpha| is a characteristic root of adj A

If A is a singular matrix, then adj A is

If A is a singular matrix then adj A is

If A is a singular matrix, then A (adj A) is a

If A is a singular matrix, then A (adj A) is a