Question

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

Answer 1

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}√(1-bc)&b\\c&-√(1-bc)\end{array}\right]`or

`\left[\begin{array}{ccc}-√(1-bc)&b\\c&√(1-bc)\end{array}\right]`