How to check kernel if 32 or 64 bit

[alex@localhost ~]$ uname -m
i686
[alex@localhost ~]$ file /usr/bin/file
/usr/bin/file: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.9, stripped
[alex@localhost ~]$