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**ulysses123** I have to find the determinant of this matrix using different properties of the determinant. We can not simply give the solution by finding it with mathematics sotware.

I have tried puting it into reduced row echelon form, but this takes ages.Is there an easier way?

Q1)Show that the determinant of the following matrix is $\displaystyle (a-b)^4$$\displaystyle (a+4b)$

$\displaystyle \begin{array}{ccccc}a&b&b&b&b\\b&a&b&b&b\\b&b&a&b& b\\b&b&b&a&b\\b&b&b&b&a\end{array}$