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Come up Guys!!

It is not as difficult as it seems .

 You virtually have to do no numerical calculation at all  for matrix inversion !!

How do u find determinant of 4th order. Think its out of syllabus. 

Put c₁=rt3c₀ and c₂=-rt3c₃  and write the matrix and it's transpose.

Now,find A.A^T,it will be equal to (4c₀²+4c₃²)I where

4(c₀²+c₃²)=1 on substituting the values and Hence A^T=A^-1

Hurrah..I am the first to solve it.

Thus,the answer is A^-1=A^T which is

Matrix c₀  c₂  c₃  c₁

           c₁  c₃ -c₂ -c₀

           c₂  c₀  c₁  c₃

           c₃  c₁ -c₀ -c₂

I'd solved this yesterday, but net went down, and I've only just been able to log on..

Anyways congratulations to allamraju..

@feynmann

By the way was that observation you were talking about this

c0^2 + c1^2 + c2^2 + c3^2 = 1

And c0 . c2 + c1. c3 = 0

Anyway, that's how I got it..

Excellent !!

Simple Problem Simple Answer !!

But Allamraju I should mention that in addition to AA' =I , we also have A'A=I(check this out !! )

That is why the inverse is A'.