For a square matrix $X$, let $\operatorname{det}(X)$ be the determinant of $X$ and let $X^T$ be the transpose of the matrix $X$. If $P$ and $Q$ are two $3 \times 3$ invertible real matrices, then the correct statement/statements is/are

• Correct answer
  A

  $\operatorname{det}(\operatorname{adj}(P))=[\operatorname{det}(P)]^2$, where $\operatorname{adj}(P)$ is the adjoint of $P$
• B

  $\operatorname{det}(c P)=c \cdot \operatorname{det}(P)$, where $c$ is a real number
• Correct answer
  C

  $\operatorname{det}\left(Q P\left(Q^T\right)^{-1}\right)=\operatorname{det}(P)$
• D

  $\operatorname{det}(P+Q)=\operatorname{det}\left(P^T\right)+\operatorname{det}(Q)$

Hence, the correct answer is options: 'A', 'C'.