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# prove that : $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = abc \bigg( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+1 \bigg) = (bc+ca+ab+abc).$

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Toolbox:
• Elementary transformation can be done by
• (i) Interchanging any two rows or column.
• (ii) The addition of elements of any row or column.
• If $A=\begin{bmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{bmatrix}$