Perform the indicated​ operation, if possible.
left bracket Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 9 2nd Row 1st Column 2 2nd Column negative 8 EndMatrix right bracket
  left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 6 2nd Column negative 1 2nd Row 1st Column negative 5 2nd Column 3 EndMatrix right bracket
 
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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 2 2nd Column 9 2nd Row 1st Column 2 2nd Column negative 8 EndMatrix right bracket
  left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 6 2nd Column negative 1 2nd Row 1st Column negative 5 2nd Column 3 EndMatrix right bracket
 equals
  
enter your response here ​(Simplify your​ answer.)
B.
The operation is not possible.

The operation indicated involves multiplying two \( 2 \times 2 \) matrices.

We are given the following matrices:

\[
A = \begin{pmatrix} 
2 & 9 \\
2 & -8 
\end{pmatrix}, \quad
B = \begin{pmatrix} 
-6 & -1 \\
-5 & 3 
\end{pmatrix}
\]

To multiply the matrices, we use the rule for matrix multiplication:

\[
(A \times B)_{ij} = \sum_{k=1}^{2} A_{ik} B_{kj}
\]

This means that each entry of the resulting matrix is the dot product of the corresponding row from the first matrix and the corresponding column from the second matrix.

Let's calculate each element of the resulting matrix.

### First row, first column:
\[
(2 \times -6) + (9 \times -5) = -12 + (-45) = -57
\]

### First row, second column:
\[
(2 \times -1) + (9 \times 3) = -2 + 27 = 25
\]

### Second row, first column:
\[
(2 \times -6) + (-8 \times -5) = -12 + 40 = 28
\]

### Second row, second column:
\[
(2 \times -1) + (-8 \times 3) = -2 + (-24) = -26
\]

Thus, the product of the two matrices is:

\[
A \times B = \begin{pmatrix} 
-57 & 25 \\
28 & -26 
\end{pmatrix}
\]

So the correct choice is:
\[
\boxed{A}
\]

Would you like further details on any of these steps or have any questions?

---

Here are 5 related questions to deepen your understanding:

1. How do you multiply two \(3 \times 3\) matrices?
2. What are the conditions for matrix multiplication to be defined?
3. Can matrix multiplication be commutative? Why or why not?
4. How do you find the determinant of a \(2 \times 2\) matrix?
5. What is the identity matrix, and how does it affect matrix multiplication?

**Tip:** Matrix multiplication is not commutative, meaning \( A \times B \neq B \times A \) in general. Always check the order!

Perform the indicated​ operation, if possible. Matrix A: [[2, 9], [2, -8]] and Matrix B: [[-6, -1], [-5, 3]]. Part 1: Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A) Matrix A × Matrix B equals [enter your response here], or B) The operation is not possible.

Solve the matrix multiplication of two 2x2 matrices. Learn how to calculate the product of Matrix A: [[2, 9], [2, -8]] and Matrix B: [[-6, -1], [-5, 3]] step-by-step. This detailed solution includes key concepts from linear algebra, matrix multiplication rules, and how to compute each element of the resulting matrix. Suitable for high school students in Grades 10-12.

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