Matter can be dead or alive.
We do not yet know what "matter" is and what "alive" means, so answering such a questions is rather difficult.
As a matter of fact she is still alive.
yes,air is a matter
As grass is or has been alive, yes. Organic matter comes from organisms, or things that are or have been alive as opposed to lifeless.
This is a matter of personal opinion.
your pumpy thing that keeps you alive!
Organic material.
Certainly not. It is a hotly debated subject. Viruses (and prions for that matter) are not alive in a conventional sense.
organic matter
yes simple as that dosent matter if dead or alive.
dead implies that it was once alive, but nonliving implies that it is simply matter, and never was alive.
In order to be alive something must take in energy, adapt to the environment, and reproduce. Smoke doesn't do that so it's not alive.