Algebra II Recipe: Identity and Inverse Matrices

A. Definitions

1. identity matrix - a matrix having 1's on the main diagonal and zeros in all other entries.
• 2x2 identity matrix
  
• 3x3 identity matrix
  
2. inverse matrices - two matrices whose product in any order is an identity matrix

B. How to Determine if Two Matrices are Inverses

1. Multiply the two matrices: AB and BA.
2. If the result is an identity matrix, then the matrices are inverses.

Practice Problems