LinAlg - Determinants/Adjoints?

If A is 3x3 and detA=2, then det(A^-1-(adjA)) = ?

I know that the answer is -(1/2)
and my teacher did it on the board, saying that adjA=(detA)(A^-1)

but I don't understand that part of it!
i'd really appreciate it if someone would explain it to me (Worried)

thanks in advance

Use these facts:

• 
• 
• where is a constant, is the size of the matrix
• ..... Can be shown here

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You should know that:

Multiply both sides by to get: