Given matrices G = [[6, 0], [-4, 2]] and H = [[9, 0], [-6, 3]], prove or disprove that 5G − 2H = 0.

Multiply each element of matrix $G$ by 5.

$$5G = 5 \begin{bmatrix} 6 & 0 \\ -4 & 2 \end{bmatrix} = \begin{bmatrix} 5 \times 6 & 5 \times 0 \\ 5 \times (-4) & 5 \times 2 \end{bmatrix} = \begin{bmatrix} 30 & 0 \\ -20 & 10 \end{bmatrix}$$

Multiply each element of matrix $H$ by 2.

$$2H = 2 \begin{bmatrix} 9 & 0 \\ -6 & 3 \end{bmatrix} = \begin{bmatrix} 2 \times 9 & 2 \times 0 \\ 2 \times (-6) & 2 \times 3 \end{bmatrix} = \begin{bmatrix} 18 & 0 \\ -12 & 6 \end{bmatrix}$$

Subtract the corresponding elements of $2H$ from $5G$.

$$5G - 2H = \begin{bmatrix} 30 & 0 \\ -20 & 10 \end{bmatrix} - \begin{bmatrix} 18 & 0 \\ -12 & 6 \end{bmatrix}$$ $$5G - 2H = \begin{bmatrix} 30 - 18 & 0 - 0 \\ -20 - (-12) & 10 - 6 \end{bmatrix}$$ $$5G - 2H = \begin{bmatrix} 12 & 0 \\ -20 + 12 & 4 \end{bmatrix}$$ $$5G - 2H = \begin{bmatrix} 12 & 0 \\ -8 & 4 \end{bmatrix}$$

The problem asks to show that $5G - 2H = 0$. However, our calculation shows that $5G - 2H = \begin{bmatrix} 12 & 0 \\ -8 & 4 \end{bmatrix}$, which is not the zero matrix $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$.

Therefore, the statement $5G - 2H = 0$ is incorrect based on the given matrices.

The final answer is $\boxed{\text{The statement } 5G - 2H = 0 \text{ is incorrect. } 5G - 2H = \begin{bmatrix} 12 & 0 \\ -8 & 4 \end{bmatrix}}$.