Determinants and inverses · Grade 11
In Grade 11 you learn: determinants.
The determinant of a square matrix is a single number. It tells you how the matrix scales area (or volume) and whether it can be undone. If the determinant is not zero, the matrix has an inverse. The inverse solves matrix equations and reverses transformations.
Key facts
- det [[a, b], [c, d]] = ad − bc.
- |det| is the area scale factor. A negative determinant means the orientation is reversed (a reflection is involved).
- det(AB) = det A × det B, and (AB)^(−1) = B^(−1)A^(−1).
- 3 × 3: expand along a row with the sign pattern + − +: a(ei − fh) − b(di − fg) + c(dh − eg).