Perform the indicated​ operation, if possible.
left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 8 2nd Column 1 2nd Row 1st Column 2 2nd Column negative 2 EndMatrix right bracket −8	1	2	−2  left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 5 2nd Column negative 3 2nd Row 1st Column negative 3 2nd Column 7 EndMatrix right bracket −5	−3	−3	7
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 8 2nd Column 1 2nd Row 1st Column 2 2nd Column negative 2 EndMatrix right bracket −8	1	2	−2  left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 5 2nd Column negative 3 2nd Row 1st Column negative 3 2nd Column 7 EndMatrix right bracket −5	−3	−3	7 equals=enter your response here ​(Simplify your​ answer.)
B.
The operation is not possible.

Let's solve this problem step by step. The given operation involves matrix multiplication.

We are asked to multiply two 2x2 matrices:

Matrix A = 
\[
\begin{bmatrix}
-8 & 1 \\
2 & -2
\end{bmatrix}
\]
and

Matrix B = 
\[
\begin{bmatrix}
-5 & -3 \\
-3 & 7
\end{bmatrix}
\]

The general rule for multiplying two matrices \( A \times B \) is:
\[
C_{ij} = \sum A_{ik} B_{kj}
\]
where \( C_{ij} \) is the element in the resulting matrix, \( A_{ik} \) is the element from matrix A, and \( B_{kj} \) is the element from matrix B.

The resulting matrix will also be 2x2.

### Step-by-step calculation:

1. **First Row, First Column**:
   \[
   (-8 \times -5) + (1 \times -3) = 40 - 3 = 37
   \]
2. **First Row, Second Column**:
   \[
   (-8 \times -3) + (1 \times 7) = 24 + 7 = 31
   \]
3. **Second Row, First Column**:
   \[
   (2 \times -5) + (-2 \times -3) = -10 + 6 = -4
   \]
4. **Second Row, Second Column**:
   \[
   (2 \times -3) + (-2 \times 7) = -6 - 14 = -20
   \]

### Resultant matrix:
\[
\begin{bmatrix}
37 & 31 \\
-4 & -20
\end{bmatrix}
\]

Thus, the answer is:
\[
\boxed{
\begin{bmatrix}
37 & 31 \\
-4 & -20
\end{bmatrix}
}
\]

Let me know if you want more details or have questions.

Here are 5 related questions:
1. How do you determine if two matrices can be multiplied?
2. What are the dimensions of the resulting matrix when multiplying two matrices?
3. Can matrix multiplication be done in any order, or is it specific (A * B ≠ B * A)?
4. How does matrix multiplication differ from scalar multiplication?
5. Can we multiply matrices of different dimensions (e.g., 2x3 with 3x2)?

**Tip**: Matrix multiplication is not commutative, meaning \( A \times B \) is not necessarily equal to \( B \times A \). Always pay attention to the order of multiplication!

Perform the indicated operation, if possible. 
Matrix A: 
[[-8, 1], [2, -2]] 
Matrix B: 
[[-5, -3], [-3, 7]] 
What is the result of multiplying these matrices?

Learn how to multiply two 2x2 matrices, [-8, 1, 2, -2] and [-5, -3, -3, 7], using matrix multiplication rules. The solution involves step-by-step calculations, resulting in the matrix [[37, 31], [-4, -20]]. Suitable for Grades 10-12.

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