Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ identity matrix. Using the above property, the determinant of the matrix given below is
$$\begin{bmatrix} 2&1 &1 &1 \\ 1&2 &1 &1 \\ 1& 1& 2& 1\\ 1&1 &1 &2 \end{bmatrix}$$
- $2$
- $5$
- $8$
- $16$
