If $$A = \left[ {\matrix{ {\cos \theta } & {i\sin \theta } \cr {i\sin \theta } & {\cos \theta } \cr } } \right]$, $\left( {\theta = {\pi \over {24}}} \right)$$ and $${A^5} = \left[ {\matrix{ a & b \cr c & d \cr } } \right]$, where $i = \sqrt { - 1} $$ then which one of the following is not true?

Question

If $$A = \left[ {\matrix{ {\cos \theta } & {i\sin \theta } \cr {i\sin \theta } & {\cos \theta } \cr } } \right]$, $\left( {\theta = {\pi \over {24}}} \right)$$

and $${A^5} = \left[ {\matrix{ a & b \cr c & d \cr } } \right]$, where $i = \sqrt { - 1} $$ then which one of the following is not true?

$a$² - $c$² = 1

$0 \le {a^2} + {b^2} \le 1$

$ a$² - $d$² = 0

${a^2} - {b^2} = {1 \over 2}$

Solution

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