If 1! + 3! + 5! + 7! + ... + 199! is divided by 24, what is the remainder?

What is the value of $\sqrt{12+5 i}+\sqrt{12-5 i}$ where $i=\sqrt{-1}$ ?

If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of det(I + AA'), where I is the 3 × 3 identity matrix?

If A, B and C are square matrices of order 3 and det(BC) = 2 det(A), then what is the value of det(2A^-1BC)?