Compute the determinant of the matrix [[1,0],[0,-1]].

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Compute the determinant of the matrix [[1,0],[0,-1]].

Explanation:
The determinant of a 2×2 matrix [[a, b], [c, d]] is ad − bc. When the matrix is diagonal like this one, the off-diagonal entries b and c are zero, so the determinant simplifies to ad. Here a is 1 and d is −1, so the determinant is 1 × (−1) = −1. Therefore, the determinant equals −1.

The determinant of a 2×2 matrix [[a, b], [c, d]] is ad − bc. When the matrix is diagonal like this one, the off-diagonal entries b and c are zero, so the determinant simplifies to ad. Here a is 1 and d is −1, so the determinant is 1 × (−1) = −1. Therefore, the determinant equals −1.

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