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Try using Gaussian elimination to transform this matrix to an upper diagonal one. Then read the determinant off as the product of the diagonal elements.
some hints Look at the matrix $\displaystyle B=A-xI$ where $\displaystyle I$ is the $\displaystyle n\times n$ identity matrix the characteristic polynomial of $\displaystyle B = det(B-xI)$ $\displaystyle B$ is a rank one matrix
Originally Posted by Idea some hints Look at the matrix $B=A-xI$ where $I$ is the $n\times n$ identity matrix the characteristic polynomial of $B = det(B-xI)$ $B$ is a rank one matrix I have replace "tex" with dollar signs.