If `A=[[1, 1,-2],[ 2, 1,-3],[ 5, 4,-9]]`. Find `|A|`.

Explanation

To find the determinant of the matrix \( A = \begin{bmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{bmatrix} \), we will use the rule of Sarrus or the cofactor expansion method. Here are the steps to calculate the determinant:

### Step 1: Write down the matrix
We start with the given matrix:
\[ A = \begin{bmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{bmatrix} \]

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