The matrix is a 2 by 2 matrix, and the determinant of the matrix by hand is -3
How to determine the determinant?
The matrix is given as:
1 2
2 1
The determinant of the matrix is calculated using the following product expression
det |A| = 1 * 1 - 2 * 2
Evaluate the product
det |A| = 1 - 4
Evaluate the difference
det |A| = -3
Hence, the determinant of the matrix by hand is -3
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