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If A = [ 0 -tan(θ/2) / tan(θ/2) 0 ] and (I2 + A)(I2 - A)^-1 = [ a -b / b a ], then 13(a^2 + b^2) is equal to ______.

1. 1
2. 13
3. 26
4. 169

Correct answer: 1

Solution

The expression (I2 + A)(I2 - A)^-1 simplifies to a form that reveals the relationship between a and b, leading to the conclusion that a^2 + b^2 equals 1. Multiplying this result by 13 gives the final answer of 13.

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