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  4. Let A = [1&a(b+c)&bc 1&b(c+a)&ca 1&c(a+b)&ab] , then det A is

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Q. Let $A = \begin{bmatrix}1&a\left(b+c\right)&bc\\ 1&b\left(c+a\right)&ca\\ 1&c\left(a+b\right)&ab\end{bmatrix} $, then det A is

Determinants

Solution:

Operate $C_2 \to C_2 + C_3$ and take out $ab + bc + ac$ from $C_2$. It will be found that $C_1 = C_2$