Let $$A = \begin{pmatrix} m & n \\ p & q \end{pmatrix}$$, $$d = |A| \neq 0$$ and $$A - d(\text{Adj } A) = 0$$. Then

A

$$1 + d^2 = (m+q)^2$$

B

$$1 + d^2 = m + q$$

C

$$1 + d^2 = m^2 + q^2$$

D

$$(1 + d)^2 = m^2 + q^2$$