Finding 2×2 Inverses

Linear Algebra (Matrices) · Axiom Academy

Derive the inverse formula, apply it to a real matrix, and verify AA^ -1 =I . Find the inverse of using the inverse formula, then verify the result by checking that . Nicely done — you derived the inverse formula, applied it to a real matrix, and confirmed it with AA^ -1 =I . The pattern to remember: The formula: — swap the diagonal , negate the off-diagonal b,c , divide by the determinant. Determinant first: compute before anything else. If the matrix is singular and has no inverse. Always verify: a correct inverse satisfies — the matrix-product check catches sign and arithmetic slips. The inverse is the workhorse behind solving , undoing linear transformations, and Cramer's rule — and the determinant is the single number that decides whether an inverse exists at all.

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.