To determine the correct answer from the given options, we need to compare the relevant matrices to see which ones are equal.
The matrices are:
[tex]\[ A = -2 \left[\begin{matrix} -6 & 4 \\ 3 & 7 \\ 12 & 10 \end{matrix}\right] \][/tex]
[tex]\[ B = 3 \left[\begin{matrix} -2 & 2 & 8 \\ 8 & 5 & 6 \end{matrix}\right] \][/tex]
[tex]\[ C = 3 \left[\begin{matrix} -2 & 8 \\ 2 & 5 \\ 8 & 6 \end{matrix}\right] \][/tex]
[tex]\[ D = -1 \left[\begin{matrix} -12 & 8 \\ 6 & 14 \\ 24 & 20 \end{matrix}\right] \][/tex]
Let's focus on comparing matrix [tex]\( A \)[/tex] and matrix [tex]\( D \)[/tex] to see if they are equal:
First, calculate matrix [tex]\( A \)[/tex]:
[tex]\[ A = -2 \left[\begin{matrix} -6 & 4 \\ 3 & 7 \\ 12 & 10 \end{matrix}\right] = \left[\begin{matrix} 12 & -8 \\ -6 & -14 \\ -24 & -20 \end{matrix}\right] \][/tex]
Next, calculate matrix [tex]\( D \)[/tex]:
[tex]\[ D = -1 \left[\begin{matrix} -12 & 8 \\ 6 & 14 \\ 24 & 20 \end{matrix}\right] = \left[\begin{matrix} 12 & -8 \\ -6 & -14 \\ -24 & -20 \end{matrix}\right] \][/tex]
As we can see, the matrices [tex]\( A \)[/tex] and [tex]\( D \)[/tex] are indeed equal. Hence, the correct answer to fill in the blank is:
[tex]\[
A \text{ and } D
\][/tex]
Therefore, the correct statement is:
[tex]\[
A=-2\left[\begin{array}{cc}
-6 & 4 \\
3 & 7 \\
12 & 10
\end{array}\right], B=3\left[\begin{array}{ccc}
-2 & 2 & 8 \\
8 & 5 & 6
\end{array}\right], 3 C=3\left[\begin{array}{cc}
-2 & 8 \\
2 & 5 \\
8 & 6
\end{array}\right] \text { and } D=-1\left[\begin{array}{cc}
-12 & 8 \\
6 & 14 \\
24 & 20
\end{array}\right]
\][/tex]
[tex]\(
\boxed{\text{A and D are equal matrices.}}
\)[/tex]
