bash string-operator problem

[Rockefeller, Harry]

CYGWIN_NT-6.1 HARRYR-PC 3.0.0(0.336/5/3) 2019-02-16 13:21 x86_64 Cygwin
GNU bash, version 4.4.12(3)-release (x86_64-unknown-cygwin)

#!/bin/bash
A="A"
B="A"
if [ $A!=$B ]; then
    echo -e "not identical"
fi
if [ $A==$B ]; then
    echo -e "identical"
fi
exit 0

Running this script gives
not identical
identical

Both tests are true.

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