Can a person with type A blood can receive a transfusion of blood types B and AB?

Short answer NO!

Type A has anti-B antibodies.
Type B has anti-A antibodies.
Type AB has no antibodies.
Type O has anti-A and anti-B antibodies.

Thus Type AB is the universal receiver can take any type in a pinch.
Type O is Universal donor.
Type A and B can only receive from their own type or type O.

There is also the problem of Rh factor Positive and Negative. A person with Rh positive can receive Rh negative or Rh positive as it is Rh negative here that carries the anti- Rh factor. Rh Negative may receive only Negative blood. Typed accordingly with the type factor above.

This makes Type O negative universal donor in any case. This is why hospitals often have a shortage of it in emergencies.

If the recipients blood type and factor are known they should receive their own type. There are also some sub-factors that are rare and poorly understood. These people can have a reaction even with a perfect type Rh factor match. But if you go into a hospital bleeding out and no Id shows what type you are you will get O Negative almost universally wasting the precious O negative in the blood supply and risking a slight reaction. This is why you should always carry a card with your exact blood type on it. O negative may not be available at the time and hospital staff may have to put you in danger while waiting for a type and cross match.

The Red Cross can give you a card with accurate match on it. Give the gift of life it can save your life.

No. A person with type A blood has antigens against type B. If a person with type A blood received a transfusion of type B or AB blood, their antigens would react with the blood and form nasty clumps.

If you have type A blood, you can only receive type A or O blood. Type B or AB blood will be attacked by your anti-B antibodies.

No. A blood types can receive from A or O. B can received from B or O. AB can receive A, B, AB or O. O blood types can only recieve from other O's. Rh factor is also important. Negatives can donated to positives but positives can not donate to negatives.

No and definitely No.