An invertible matrix has the property AA−1=A−1A=I.
Use matrix multiplication and the identity to find the inverse of a 2×2 matrix.
The multiplicative inverse can be found using a formula.
Another method of finding the inverse is by augmenting with the identity.
We can augment a 3×3 matrix with the identity on the right and use row operations to turn the original matrix into the identity, and the matrix on the right becomes the inverse.
Write the system of equations as AX=B, and multiply both sides by the inverse of A:A−1AX=A−1B.
We can also use a calculator to solve a system of equations with matrix inverses.
Glossary
identity matrix
a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra
multiplicative inverse of a matrix
a matrix that, when multiplied by the original, equals the identity matrix