8.9. Inverse Matrices http://www.ck12.org
A·A−^1 =A·B
A−^1 ·
96
36
− 12
=B·
96
36
− 12
=B·C
You need to create matrixC=
96
36
− 12
Being able to effectively use a calculator should improve your understanding of matrices and allow you to check all
the work you do by hand.
- Helmert came up with a very clever matrix that happens to be its own inverse. Here are the 2×2 and the
3 ×3 versions.
√^1
2
√^1
1 2
√ 2 −√^12
,
√^1
3
√^1
3
√^1
1 3
√ 2 −√^120
√^1
6
√^1
6 −
√^2
6
Practice
Find the inverse of each of the following matrices, if possible. Make sure to do some by hand and some with your
calculator.