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Question
If `"A" = [(a , b),(c , d)] and "I" = [(1 , 0),(0 , 1)]` show that A2 - (a + d) A = (bc - ad) I.
Solution
Here A2 - (a + d) A
= `[(a , b),(c , d)][(a , b),(c , d)] -(a + d)[(a , b),(c ,d)]`
= `[(a^2 + bc , ab + bd),(ac + dc, cb + d^2)] - [(a^2 + ad , ab + bd),(ac + dc , ad + d^2)]`
= `[(bc - ad , 0),(0 , bc -ad)] = (bc - ad)[(1 , 0),(0 , 1)]`
= (bc - ad) I.
Hence proved.
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