If Delta _1 = left| begin{matrix} b^5c^6(c^3 | vedclass

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(A) Let $\Delta_2 = \begin{vmatrix} a & b^2 & c^3 \ a^4 & b^5 & c^6 \ a^7 & b^8 & c^9 \end{vmatrix}$.The determinant $\Delta_1$ is the cofactor matr

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$\Delta _2^3$

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(A) Let $\Delta_2 = \begin{vmatrix} a & b^2 & c^3 \ a^4 & b^5 & c^6 \ a^7 & b^8 & c^9 \end{vmatrix}$.The determinant $\Delta_1$ is the cofactor matrix determinant of $\Delta_2$. According to the property of determinants,if $\Delta_1$ is the determinant of the cofactor matrix of $\Delta_2$,then $\Delta_1 = (\Delta_2)^{n-1}$,where $n$ is the order of the matrix.Here,the order of the matrix is $n = 3$,so $\Delta_1 = (\Delta_2)^{3-1} = \Delta_2^2$.Therefore,$\Delta_1 \Delta_2 = \Delta_2^2 \cdot \Delta_2 = \Delta_2^3$.

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