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To solve for the product of the matrices \( X \) and \( Y \), where:

\[
X = [-1 \quad 0] \quad \text{and} \quad Y = \begin{bmatrix} -2 \\ -1 \end{bmatrix}
\]

We perform the matrix multiplication \( XY \).

1. \( X \) is a 1x2 matrix, and \( Y \) is a 2x1 matrix.
2. The result of multiplying a 1x2 matrix by a 2x1 matrix is a 1x1 matrix (a scalar value).

### Matrix Multiplication:

\[
XY = [-1 \quad 0] \times \begin{bmatrix} -2 \\ -1 \end{bmatrix}
\]

This results in:

\[
XY = (-1 \times -2) + (0 \times -1) = 2 + 0 = 2
\]

Therefore, the product \( XY = 2 \).

The correct answer is **D**: \([2]\).

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Would you like further details or clarifications on this solution?

Here are some related questions you might explore:
1. What are the rules for matrix multiplication?
2. Can you multiply two matrices of any size?
3. What is the difference between scalar multiplication and matrix multiplication?
4. How does matrix multiplication relate to linear transformations?
5. What happens when you multiply a matrix by the identity matrix?

**Tip:** Always ensure that the number of columns in the first matrix matches the number of rows in the second matrix before multiplying.

Given matrices X = [-1 0] and Y = [ -2 -1], which of the following matrices is XY?

Solve the matrix multiplication problem involving X = [-1 0] and Y = [-2 -1]. This detailed step-by-step solution covers essential concepts in matrix multiplication, including matrix size compatibility and element-wise products. Suitable for students in Grades 9-12.

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