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(B) Let $\Delta = \left| \begin{array}{ccc} a & a + b & a + 2b \ a + 2b & a & a + b \ a + b & a + 2b & a \end{array} ight|$.Applying the operation

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$9b^2(a + b)$

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(B) Let $\Delta = \left| \begin{array}{ccc} a & a + b & a + 2b \ a + 2b & a & a + b \ a + b & a + 2b & a \end{array} ight|$.Applying the operation $C_1 	o C_1 + C_2 + C_3$,we get:$\Delta = \left| \begin{array}{ccc} 3a + 3b & a + b & a + 2b \ 3a + 3b & a & a + b \ 3a + 3b & a + 2b & a \end{array} ight|$Taking $3(a + b)$ common from $C_1$:$\Delta = 3(a + b) \left| \begin{array}{ccc} 1 & a + b & a + 2b \ 1 & a & a + b \ 1 & a + 2b & a \end{array} ight|$Applying $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$:$\Delta = 3(a + b) \left| \begin{array}{ccc} 1 & a + b & a + 2b \ 0 & -b & -b \ 0 & b & -2b \end{array} ight|$Expanding along $C_1$:$\Delta = 3(a + b) [(-b)(-2b) - (-b)(b)]$$\Delta = 3(a + b) [2b^2 + b^2] = 3(a + b)(3b^2) = 9b^2(a + b)$.

The value of $\left| \begin{array}{ccc} a & a + b & a + 2b \\ a + 2b & a & a + b \\ a + b & a + 2b & a \end{array} \right|$ is equal to

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