Sunday, 18 August 2013

4th power of a 2X2 matrix

4th power of a 2X2 matrix

A = [cosx -sinx; sinx cosx ] is given as a matrix. What is the result of
a.d + b.c if A^4=[a b ; c d] .
Note that A^4 is the 4th power of the matrix A.
I tried to use some trigonometric expressions but it gets very complicated
and couldnt solve it.

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