The determinant of the matrix given in the image is -61
Determinant of matrix
A = -2 2 -5
4 -1. -2
1 3 -5
A = -2{(-5× -1) - (3 × -2)} + -2{(-5×4) - (-2×1)} + -5{(4×3) - (-1×2)}
= -2{(5-(-6)} + -2{(-20 -(-2)} + -5{(12-(-2)}
= -2(5 + 6) + -2(-20+2) + -5(12+2)
= -2(11) + -2(-18) + -5(14)
= -22 + 36 -75
= -61
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