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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.
Solution
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.
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