# Symmetric matrices maybe

1. Jul 20, 2009

### chaotixmonjuish

I had this question on a test and I was wondering why it is false:

If the row space equals teh column space then AT=A.

2. Jul 20, 2009

### slider142

Consider the matrix
$$\left(\begin{array}{cc}1 & 1\\0 & 1\end{array}\right)$$.

3. Jul 20, 2009

### chaotixmonjuish

Ok, so I had a rationale why it was false but I'm not sure if I am close.

Obviously here the AT does not equal A, but the dimension of the row space equals column space equals 2. Is this the right reasoning?

4. Jul 20, 2009

### slider142

Well, the row space and the column space are both R2, but the matrix is not symmetric.