Determinant & Inverse

Find determinants and inverse matrices for 2×2 and 3×3 matrices, and solve systems with Cramer’s rule, with each cofactor shown. Try “inverse of [[2,1],[5,3]]”.

Try an example:

How the Determinant & Inverse works

  1. Determinant of a 2×2: ad − bc = 2×3 − 1×5 = 1.
  2. If the determinant is zero, the matrix has no inverse.
  3. Inverse = 1/det × [[d, −b], [−c, a]] = [[3, −1], [−5, 2]].

Frequently asked questions

When does a matrix have no inverse?

When its determinant is 0 (it is singular).

How do I check an inverse?

Multiply A by A⁻¹. You should get the identity matrix.

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