The Jacobian Matrix of the System $x ^ { \prime } = x ^ { 3 } - y ^ { 3 } - 8 , y ^ { \prime } = 8 y$

Multiple Choice

The Jacobian matrix of the system $x ^ { \prime } = x ^ { 3 } - y ^ { 3 } - 8 , y ^ { \prime } = 8 y$ at the critical point $( 2,0 )$

A) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & - 3 y ^ { 2 } \\8 & 0\end{array} \right]$
B) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & - 3 y ^ { 2 } \\0 & 8\end{array} \right]$
C) $A = \left[ \begin{array} { r r } 3 x ^ { 2 } & 3 y ^ { 2 } \\0 & 8\end{array} \right]$
D) $A = \left[ \begin{array} { c c } 12 & 0 \\0 & 8\end{array} \right]$
E) $A = \left[ \begin{array} { c c } 12 & 0 \\8 & 0\end{array} \right]$