4. Let $A = \left[ \begin{array} { l l } a & b \\ c & d \end{array} \right]$ be a real matrix which satisfies $A ^ { - 1 } = A$. Which of the following statements is/are always true?\\
(a) $a + d = 0$\\
(b) $a d - b c = 1$\\
(c) $a d - b c \neq 0$\\
(d) $a ^ { 2 } + 2 b c + d ^ { 2 } = 2$\\