Originally Posted by

**gate13** Good day to all. I apologize if the question asked appears to be a waste of time but it has created some problems for me. In one of my end of chapter exercises I am asked the following:

**Find all 2x2 matrices where AA^T (transpose of A) = I**

I proceeded with the general equation of A such that

A= [[a,b],[c,d]] where [a,b],[c,d] are the rows of A

A^T = [[a,c],[b,d]]

After AA^T was computed I retrieved the following three equations:

(1) a^2 + b^2 = 1

(2) ac + bd = 0

(3) c^2 + d^2 =1

My first question is this a good method to follow in answering the question? My second question is that I am not sure what conclusions to draw from here (aside that AA^T is symmetric). The other problem is that we have not explicitly covered orthogonal matrices or inverses which are topics I encountered when reading other textbooks about this matter. Any help would be greatly appreciated.

Kindest regards