Finding the Inverse of [3 2; 5 4]

Algebra 2 · Axiom Academy

EXAMPLE Finding the Inverse of Apply the inverse formula step by step, then verify the result. Find the inverse of the matrix using the inverse formula. Nice work — you found the inverse of a matrix using the shortcut formula. The pieces worth keeping: Check the determinant first: if , the matrix is singular and has no inverse. Three moves: swap the diagonal, negate the off-diagonal, then scale by . Always verify: multiply and confirm you get the identity matrix I . This shortcut only works for matrices — larger matrices need row reduction or the adjugate method instead.

This is the written version of the interactive lesson above. See the full Algebra 2 course.