Regular Expressions 101

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/
^((0[1-9]|1[0-2])|([1-9]{1}))\/([0-9]{4}|[0-9]{2})$
/
mg
^ asserts position at start of a line
1st Capturing Group
((0[1-9]|1[0-2])|([1-9]{1}))
1st Alternative
(0[1-9]|1[0-2])
2nd Capturing Group
(0[1-9]|1[0-2])
1st Alternative
0[1-9]
0 matches the character 0 with index 4810 (3016 or 608) literally (case sensitive)
Match a single character present in the list below
[1-9]
1-9 matches a single character in the range between 1 (index 49) and 9 (index 57) (case sensitive)
2nd Alternative
1[0-2]
1 matches the character 1 with index 4910 (3116 or 618) literally (case sensitive)
Match a single character present in the list below
[0-2]
0-2 matches a single character in the range between 0 (index 48) and 2 (index 50) (case sensitive)
2nd Alternative
([1-9]{1})
3rd Capturing Group
([1-9]{1})
Match a single character present in the list below
[1-9]
{1} matches the previous token exactly one time (meaningless quantifier)
1-9 matches a single character in the range between 1 (index 49) and 9 (index 57) (case sensitive)
\/ matches the character / with index 4710 (2F16 or 578) literally (case sensitive)
4th Capturing Group
([0-9]{4}|[0-9]{2})
1st Alternative
[0-9]{4}
Match a single character present in the list below
[0-9]
{4} matches the previous token exactly 4 times
0-9 matches a single character in the range between 0 (index 48) and 9 (index 57) (case sensitive)
2nd Alternative
[0-9]{2}
Match a single character present in the list below
[0-9]
{2} matches the previous token exactly 2 times
0-9 matches a single character in the range between 0 (index 48) and 9 (index 57) (case sensitive)
$ asserts position at the end of a line
Global pattern flags
m modifier: multi line. Causes ^ and $ to match the begin/end of each line (not only begin/end of string)
g modifier: global. All matches (don't return after first match)
Your regular expression does not match the subject string.

Regular Expression
No Match

/
/
mg

Test String