Question

Let $A$ be a $3 \times 3$ real matrix. Suppose that 1 and 2 are characteristic roots of $A$, and 12 is a characteristic root of $A + A^2$. Then which of the following statements is/are correct?

• A. $\det(A) \neq 0$
• B. $\det(A + A^2) \neq 0$
• C. $\det(A) = 0$
• D. trace of $(A + A^2)$ is 20

Answer 1

Answer: (A), (B), (D)

$\det(A) \neq 0$

Answer 2

The correct option is (A): $\det(A) \neq 0$,(B): $\det(A + A^2) \neq 0$ ,(D): trace of $(A + A^2)$ is 20