# Homework Help: Show that if a is any m x n matrix, then ImA = A and AIn = A

1. Oct 7, 2009

### nietzsche

1. The problem statement, all variables and given/known data

Show that if A is any m x n matrix, then the m x m identity multiplied by A = A, and A multiplied by the n x n identity = A.

2. Relevant equations

3. The attempt at a solution

I know how to prove this by writing out a general m x n matrix, and multiplying it by the identity, but is there a better way of showing this? It just seems kind of silly when I write it out...

2. Oct 7, 2009

3. Oct 7, 2009

### JG89

I can`t really think of another way. The cleanest way I can think of:

$$(AI)_{i,j } = \sum_{r= 1}^n A_{i, r} I_{r, j} = a_{i, j}$$