What is the determinant of cap A is equal to the 3 by 3 matrix, row 1, column 1, negative 2 column 2, 2 column 3, negative 5 row 2, column 1, 4 column 2, negative 1 column 3, negative 2 row 3, column 1, 1 column 2, 3 column 3, negative 5 ?

For a 3 × 3 matrix, expand the determinant along the first row: (−2)[(−1)(−5) − (−2)(3)] − 2[(4)(−5) − (−2)(1)] + (−5)[(4)(3) − (−1)(1)]. This gives −22 + 36 − 65 = −51. The determinant is −51, choice D.

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