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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 

$$\begin{bmatrix} 2&1 &1 &1 \\ 1&2 &1 &1 \\ 1& 1& 2& 1\\ 1&1 &1 &2 \end{bmatrix}$$

  1. $2$
  2. $5$
  3. $8$
  4. $16$
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