Answer:
Step-by-step explanation:
Let A be a two x two matrix
A = a b
c d
|[tex]|A|=ad-bc\\det|AA inverse| = 1:i.e. (ad-bc)^2 =1[/tex], if A is its own inverse
Or ad-bc = ±1
ad-bc =1 gives a=d and b = =b and c=-c
If ad-bc =-1 then a=-d, d=-a
Hence the matrices would be of the form
[tex]\left[\begin{array}{ccc}\sqrt{1-bc}&b\\c&-\sqrt{1-bc}\end{array}\right][/tex]or
[tex]\left[\begin{array}{ccc}-\sqrt{1-bc}&b\\c&\sqrt{1-bc}\end{array}\right][/tex]
