For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc. [[3, 1], [2, 4]] has determinant 12 − 2 = 10. Matrices as a set are in matrices.
Cross-multiply, then subtract
A zero determinant means the rows are dependent and the matrix has no inverse. Complex numbers are a different leftover algebra topic, in complex numbers. i² is the small identity inside that topic, in i squared.
The short list is in ACT Math formulas.
The bottom line
2×2 determinant: ad − bc. Do not add the diagonal.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.