Proving that matrix A is unitary and find its inverse.

[zacl79]

Show the following matrix A is unitary and find its inverse.

A = 1-2i, 2i
-2i, -1-2i

Ok, i have read over this sort of thing in my textbook, and it has an example, but i can't see where the numbers in the inverse come from.

The textbook got two row vectors r1 and r2, then took their length and then their dot product. To me it seems almost like magic from where the numbers in the inverse came from.

Can someone explain the way in which you answer this question in simple terms, out lecturer doesn't cover this, but it is an extension in the assignment he has given us.

Thanks Zac

 

[Apphysicist]

A^-1 =[ 1/det(A) ]* C^T

C^T is the transpose of the matrix of cofactors...read about cofactors for a clearer definition than I have time to write.