Question

Find all 2 × 2 matrices A such that det A−1 and A = A-1

Answer 1

Answer:

Step-by-step explanation:

Let A be a two x two matrix

A = a b

     c   d

|$|A|=ad-bc\\det|AA inverse| = 1:i.e. (ad-bc)^2 =1$, 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

$\left[\begin{array}{ccc}\sqrt{1-bc}&b\\c&-\sqrt{1-bc}\end{array}\right]$or

$\left[\begin{array}{ccc}-\sqrt{1-bc}&b\\c&\sqrt{1-bc}\end{array}\right]$