[bash] Shell equality operators (=, ==, -eq)

Several answers show dangerous examples. OP's example [ $a == $b ] specifically used unquoted variable substitution (as of Oct '17 edit). For [...] that is safe for string equality.

But if you're going to enumerate alternatives like [[...]], you must inform also that the right-hand-side must be quoted. If not quoted, it is a pattern match! (From bash man page: "Any part of the pattern may be quoted to force it to be matched as a string.").

Here in bash, the two statements yielding "yes" are pattern matching, other three are string equality:

$ rht="A*"
$ lft="AB"
$ [ $lft = $rht ] && echo yes
$ [ $lft == $rht ] && echo yes
$ [[ $lft = $rht ]] && echo yes
yes
$ [[ $lft == $rht ]] && echo yes
yes
$ [[ $lft == "$rht" ]] && echo yes
$