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Easy: 2 × 2 matrices
For a 2 × 2 matrix the determinant is ad − bc: the product down the main diagonal minus the product down the other one. For a 3 × 3 matrix, expand along the first row: each entry times the 2 × 2 determinant left when its row and column are crossed out, with the signs +, −, +.
Find the determinant.
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Multiply down the main diagonal and subtract the product of the other diagonal: det[a, b; c, d] = ad − bc.
Expansion along the first row uses the pattern +, −, +: each entry times its 2 × 2 minor, with the middle term subtracted.
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