Identity matrix

1. Sep 3, 2006

EvLer

Is the identity matrix (or multiple of) the only one that commutes with other matrices or are there other matrices that AB=BA?

Thanks

2. Sep 3, 2006

StatusX

Yes, those are the only ones that commute with all other matrices. There are pairs of matrices which aren't multiples of the identity matrix that commute with each other, like any matrix with a multiple or power of itself, or:

$$\left[ \begin{array}{cc}0 & 1 \\ 1 & 0 \end{array} \right], \left[ \begin{array}{cc}a & b \\ b & a \end{array} \right]$$

but they won't commute with an arbitrary matrix.

Last edited: Sep 3, 2006
3. Sep 3, 2006

loom91

The identity matrix commutes only when both IA and AI are defined.