Question

Let A be a 2 x 2 matrix and let I be an identity matrix of the order 2 x 2. Prove that AI = IA = A. 

Answer 1

Let A = `|("p" , "q"),("r" , "s")|_(2 xx 2)`

AI = `|("p" , "q"),("r" , "s")| |(1 , 0),(0 , 1)|`

`= |("p" + 0 , 0 + "q") , ("r" + 0, 0 + "s")|` 

`= |("p" , "q"),("r" , "s")| = "A"`

IA = `|(1 , 0),(0 , 1)| |("p" , "q"),("r" , "s")|`

= `|("p" + 0 ,"q" + 0) , (0 + "r", 0 + "s")|` 

`= |("p" , "q"),("r" , "s")| = "a"`

Hence proved A l = I A = A.