linear algebra - Should the formula for the inverse of a 2x2 matrix be obvious?

pr.chance – Quantum Computing, measuring whirl down? Answer

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pr.chance – Quantum Computing, measuring whirl down?

I’m learning Quantum Computing and the lecturers slides aren’t actually valid, within the sense that we do not get any examples which may probably ameliorate (in my view that’s).

An instance rehearse is given within the slides:

We occupy the benchmark foundation for spins, whereby the absolute "spin up" condition is given by 
(1
 0).
Assume now that you're given a particle in condition 
|ψ⟩=
(1/2
i√3/2),
What is the chance to touchstone whirl down within the z course.
Express your outcome utilizing a decimal quantity.

Can somebody delight ameliorate me design this out? Possibly step-by-step? I’m actually caught and I do know this may come up within the exams.

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