D=[(0, ab^2, c^2a),(a^2b, 0, bc^2),(a^2c,b^2c,0)] =? 

Explanation:

Another Explanation (5): নির্ণায়কের মান নির্ণয়: \( D=\begin{vmatrix} 0 & ab^2 & c^2a \\ a^2b & 0 & bc^2 \\ a^2c & b^2c & 0 \end{vmatrix} \) \( D = 0 \cdot \begin{vmatrix} 0 & bc^2 \\ b^2c & 0 \end{vmatrix} - ab^2 \cdot \begin{vmatrix} a^2b & bc^2 \\ a^2c & 0 \end{vmatrix} + c^2a \cdot \begin{vmatrix} a^2b & 0 \\ a^2c & b^2c \end{vmatrix} \) \( = 0 - ab^2 (a^2b \cdot 0 - bc^2 \cdot a^2c) + c^2a (a^2b \cdot b^2c - 0 \cdot a^2c) \) \( = - ab^2 (-a^2bc^3) + c^2a (a^2b^3c) \) \( = a^3b^3c^3 + a^3b^3c^3 \) \( = 2a^3b^3c^3 \) 🎉