Find the determinant of the matrix.
0	9
1	0

The determinant of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) is calculated using the formula:

\[
\text{Determinant} = ad - bc
\]

For the given matrix:

\[
\begin{pmatrix} 0 & 9 \\ 1 & 0 \end{pmatrix}
\]

Substituting the values into the formula:

\[
\text{Determinant} = (0)(0) - (9)(1) = 0 - 9 = -9
\]

So, the determinant of the matrix is \(-9\).

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Here are 5 related questions:
1. What is the determinant of the matrix \(\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}\)?
2. How does changing one element of a matrix affect its determinant?
3. What is the geometric interpretation of the determinant of a 2x2 matrix?
4. How do you find the determinant of a 3x3 matrix?
5. What does it mean if the determinant of a matrix is zero?

**Tip:** The determinant of a matrix can indicate whether a system of linear equations has a unique solution. If the determinant is zero, the system may not have a unique solution.

Learn how to calculate the determinant of a 2x2 matrix with the values 0, 9, 1, and 0 using the determinant formula. This problem involves basic matrix algebra and determinants, suitable for high school students.

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