What is the determinant of cap A is equal to the 2 by 2 matrix, row 1, column 1, 3 column 2, 1 row 2, column 1, 11 column 2, negative 1 ?

For a 2 by 2 matrix, the determinant is the top-left entry times the bottom-right entry, minus the top-right entry times the bottom-left entry. Here, that is 3 × (−1) − 1 × 11 = −3 − 11 = −14, so the determinant is negative 14.

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