Question

Let A be an m x n matrix and B an n x m matrix, It is given that determinant $(I_m+AB)$ = determinant $(I_n+BA)$, where $I_x$ is the k $\chi$ k identity matrix. Using the above property, the determinant of the matrixgiven below is $\left[\begin{array}{cccc}2& 1& 1& 1\\ 1& 2& 1& 1\\ 1& 1& 2& 1\\ 1& 1& 1& 2\end{array}\right]$

• A. 2
• B. 5
• C. 8
• D. 16

Answer 1

The correct option is B 5

Without using property just find the determinant by usual method.