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)?

If the nth term of a sequence is $\frac{2 n+5}{7}$, then what is the sum of its first 140 terms? 

Let A be a skew-symmetric matrix of order 3.

What is the value of det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I)  where I is the identity matrix of order 3?