Expectation value of an operator in matrix quantum mechanics

[Dixanadu]

Homework Statement

Hey everyone.
Imma type this up in Word as usual:

http://imageshack.com/a/img577/3654/q9ey.jpg

Homework Equations

http://imageshack.com/a/img22/3185/pfre.jpg

The Attempt at a Solution

http://imageshack.com/a/img703/8571/xogb.jpg

 

[vanhees71]

There's a mistake in the last step. You've overlooked the imaginary units in the exponentials!

 

[Dixanadu]

Ohhh yea it isn't $cosh$, it should be $cos$...but is the rest okay? I mean the matrix U and stuff?