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I have installed Ubuntu 14.04 LTS 64bit, and would like to make sure that TRIM is enabled (as much as I know - it is enabled by default). Is there some sort of command which would help me to find out if it is working correctly?

You can perform a sudo fstrim -v / (replace "/" with other mountpoints, if you have any), to check if fstrim gives any errors.
If it doesn't, type in cat /etc/cron.weekly/fstrim which should give you an output like:

#!/bin/sh

# call fstrim-all to trim all mounted file systems which support it

set -e

#

# This only runs on Intel and Samsung SSDs by default, as some SSDs with

# faulty firmware may encounter data loss when running fstrim under high I/O

# load (e. g.  https://launchpad.net/bugs/1259829). You can append the

# --no-model-check option here to disable the vendor check and run fstrim on

# all SSD drives Like this (remove the hash):

#exec fstrim-all --no-model-check

exec fstrim-all

If it does, it means, that your Ubuntu automatically recognized that you have an SSD and will trim it once a week as a cron job.

If you like to optimize your system for SSD, check out this article.

I would suggest that a more direct, if somewhat more complex, way to ensure that trim is working is by creating a file, identifying precisely where this file is stored, checking the contents of the file at this location, deleting the file, and then re-checking the contents of the file's location. If trim is working, the original contents of the file will have been replaced by zeros. The method and the specific commands to conduct this test are documented at: http://andyduffell.com/techblog/?p=852. A specific example of the technique is provided at: https://linuxnorth.wordpress.com/2014/03/18/trim-your-ssd-down-to-size/

On 18.04, you may check it in syslog:

cat /var/log/syslog | grep -a fstrim | tail

if you see recent dates and all your SSD's mountpoints, it's working. Sample output:

Oct  1 14:54:55 justapc fstrim[769]: /home: 80,1 GiB (86008037376 bytes) trimmed

Oct  1 14:54:55 justapc fstrim[769]: /boot: 360,2 MiB (377663488 bytes) trimmed

Oct  1 14:54:55 justapc fstrim[769]: /: 16,3 GiB (17486880768 bytes) trimmed

Oct  8 08:16:01 justapc fstrim[792]: /home: 76,8 GiB (82423615488 bytes) trimmed

Oct  8 08:16:01 justapc fstrim[792]: /boot: 360,1 MiB (377634816 bytes) trimmed

Oct  8 08:16:01 justapc fstrim[792]: /: 15,9 GiB (17038168064 bytes) trimmed

Oct  8 08:16:44 justapc ureadahead[283]: ureadahead:trimage_trimage.png: Ignored relative path

Oct 15 20:14:00 justapc fstrim[749]: /home: 73,5 GiB (78863814656 bytes) trimmed

Oct 15 20:14:00 justapc fstrim[749]: /boot: 360,1 MiB (377634816 bytes) trimmed

Oct 15 20:14:00 justapc fstrim[749]: /: 16 GiB (17104076800 bytes) trimmed

To be sure of any possible errors, verbose fstrim manually:

for mountpoint in $(cat /etc/fstab | awk '/ext[0-9]/ {print $2}'); do sudo fstrim -v "$mountpoint"; done