Linear Transformation Find a which S⊕T=H

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how are you? I have a question with this exercise. enter image description here They ask me to find all the values ​​of a∈R for which S⊕T=H is:

They give me 4 options:

enter image description here

I dial {4,-4} but a friend tells me that I am wrong that it is only {-4}. Could you explain why? and who is right hahaha