PUNE MCA Exam 2014 Question Paper with answers for online practice

Concept:Use the given matrix equation $A^2 + A + 2I = 0$ to check each option.Explanation:• From $A^2 + A + 2I = 0$, we get $A(A + I) = -2I$.• Since $A$ has an inverse $A^{-1} = -\frac{1}{2}(A+I)$, $A$ is non‑singular. So option A is correct.• The inverse matches option D, so D is correct.• Because $A$ is invertible, $A \neq 0$; thus option B (interpreted as $A \neq 0$) is true.• The equation does not require $A$ to be symmetric. For a real matrix, the eigenvalues satisfy $\lambda^2+\lambda+2=0$, which has complex roots. A real symmetric matrix has real eigenvalues, so it cannot satisfy the equation. Hence option C is incorrect.Answer:Option C is incorrect.