## Algebra## More Algebra |

## What happens when you multiply a matrix by the identity matrix? |

When you multiply any *n*-by-*n* matrix by the identity matrix, you get that same matrix back again. Therefore, let the letter *I* represent the *n*-by-*n* identity matrix, and *A* represent any other *n-by-n* matrix; then we have *A* × *I* = *A* and *I* × *A* = *A.* This is much like the situation in the real numbers: *x* × 1 = *x* and 1 × *x* = *x.*