exam Maths Puzzle Numerical Ability

Let u and v be vectors in Rn, and let T be a linear operator on Rn. Prove that T(n).T(v)=n.v if and only if A(transpose)=A(inverse), where A is the standard matrix for T.

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I can not figure this problem out could someone please help?

Find the term in the sequence: 1/2, -4, 32, _
Solve the system of linear equations graphycally:

2x-4y=8
1/2x+y=-4