Determinant of a 2×2 matrix can be calculated using the following formula:

For a matrix:

\[
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\]

The determinant, denoted as \( \text{det}(A) \), is given by:

\[
\text{det}(A) = (a \times d) - (b \times c)
\]

### Example:
For the matrix:

\[
\begin{pmatrix}
2 & 3 \\
4 & 5
\end{pmatrix}
\]

The determinant is:

\[
\text{det}(A) = (2 \times 5) - (3 \times 4) = 10 - 12 = -2
\]

Would you like further details on the determinant calculation, or do you have any questions?

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Here are some related questions:
1. How do you calculate the determinant for a 3×3 matrix?
2. What are some applications of the determinant in linear algebra?
3. What does it mean when the determinant of a matrix is zero?
4. How can you compute the determinant of larger matrices using cofactor expansion?
5. What is the geometric interpretation of the determinant of a matrix?

**Tip:** The determinant of a 2×2 matrix tells you the area scaling factor when the matrix is applied as a transformation on a plane.

Learn how to calculate the determinant of a 2×2 matrix with the formula det(A) = (a × d) - (b × c). This example uses the matrix [2, 3; 4, 5] and walks through the steps to find the determinant. Suitable for students in Grades 9-12.

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