Comparing strings

I have two strings
a=Mar22
b=may21

how can I compare them
Is this fine

if[ $a -eq $b ] then;
.
...

else
....
fi

or
if[ $a = $b ] then

for string comparisions we generally use = operator.
-eq is used for integer comparisons.
if [ "str1" = "str2" ] then

fi

will do your task .

Many Thanks.It worked now. I tried with out " ".