I am an A&P with Inspection Authorization.

A&P means Airframe and Powerplant Licenses. You could have either one
or both e.g. "A" license for airframe only.

After having both for and actively working in the field for 36 months,
you can test for the IA - Inspection authorization. I am also a pilot
with a type rating and the IA test, when I took it in 1972, was far
and away the hardest one ever.

The IA is essentially a small aircraft ticket, because it allows you
to inspect and sign off an annual inspection. You also have limited
ability to sign an FAA form 337, Major Repair or Alteration. Large
aircraft do not have annuals so an IA is not required.

That being said, many of my compatriots have received their IA as we
consider it a feather in our cap to hold. By the way, the A&P is good
for life, but we have to get the IA renewed annually. This requires a
certain amount of education or activity with annuals or 337's. Since
large aircraft don't get annuals, in my field, we all get an annual
class.