Evaluate : `|{:(-2,3),(4,-9):}|`

Answer

To evaluate the determinant of the given 2x2 matrix \(\begin{pmatrix} -2 & 3 \\ 4 & -9 \end{pmatrix}\), we will use the formula for the determinant of a 2x2 matrix:

\[ |A| = ad - bc \]

where \(A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}\). In our case:

- \(a = -2\)
- \(b = 3\)
- \(c = 4\)
- \(d = -9\)

Now, we can substitute these values into the determinant formula:

1. **Calculate \(ad\)**:
\[ ad = (-2) \times (-9) = 18 \]

2. **Calculate \(bc\)**:
\[ bc = (3) \times (4) = 12 \]

3. **Subtract \(bc\) from \(ad\)**:
\[ |A| = ad - bc = 18 - 12 = 6 \]

Thus, the value of the determinant is:

\[ \boxed{6} \]