Question

Let $A = \begin{pmatrix} a & 0 \\\ c & d \end{pmatrix}$ be a real matrix, where $ad = 1$ and $c \ne 0$. If $A^{-1} + (\text{adj} \, A)^{-1} = \begin{pmatrix} \alpha & \beta \\\ \gamma & \delta \end{pmatrix}$, then $(\alpha, \beta, \gamma, \delta)$ is equal to

• A. $(a + d, 0, 0, a + d)$
• B. $(a + d, 0, c, a + d)$
• C. $(a, 0, 0, d)$
• D. $(a, 0, c, d)$

Answer 1

Answer: (A)

$(a + d, 0, 0, a + d)$

Answer 2

The correct option is (A): $(a + d, 0, 0, a + d)$