Answer:
A and D are equal matrices
Step-by-step explanation:
Two matrices are equal if they have the same dimensions (numbers of rows and columns)
∵ ![A=-2\left[\begin{array}{cc}-6&4\\3&7\\12&10\end{array}\right]](https://tex.z-dn.net/?f=A%3D-2%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-6%264%5C%5C3%267%5C%5C12%2610%5Cend%7Barray%7D%5Cright%5D)
- Multiply each element by -2
∴ ![A=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12%26-8%5C%5C-6%26-14%5C%5C-24%26-20%5Cend%7Barray%7D%5Cright%5D)
∵ Matrix A has 3 rows and 2 columns
∴ Its dimensions are 3 × 2
∵ Matrix B has 2 rows and 3 columns
∴ Its dimensions are 2 × 3
- Equal matrices has equal dimensions and equal corresponding
elements
∵ A and B has different dimensions, so they can not be equal
∴ A ≠ B
∵ ![3C=3\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right]](https://tex.z-dn.net/?f=3C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%268%5C%5C2%265%5C%5C8%266%5Cend%7Barray%7D%5Cright%5D)
∴ The dimensions of C are 3 × 2
- Divide the two sides of the matrix by 3 to find C
∴ ![C=\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right]](https://tex.z-dn.net/?f=C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%268%5C%5C2%265%5C%5C8%266%5Cend%7Barray%7D%5Cright%5D)
∵ A and C have same dimensions but they have different
corresponding elements
∴ A ≠ C
∵ ![D=-1\left[\begin{array}{cc}-12&8\\6&14\\24&20\end{array}\right]](https://tex.z-dn.net/?f=D%3D-1%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-12%268%5C%5C6%2614%5C%5C24%2620%5Cend%7Barray%7D%5Cright%5D)
- Multiply each element by -1
∴ ![D=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right]](https://tex.z-dn.net/?f=D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12%26-8%5C%5C-6%26-14%5C%5C-24%26-20%5Cend%7Barray%7D%5Cright%5D)
∵ The dimensions of D are 3 × 2
∵ The corresponding elements of A and D are equal
∴ A and D are equal matrices