Answer :

Here,

Now, we have to find adj A and for that we have to find co-factors:


a11 (co – factor of 3) = (-1)1+1(2) = (-1)2(2) = 2


a12 (co – factor of -5) = (-1)1+2(-1) = (-1)3(-1) = 1


a21 (co – factor of -1) = (-1)2+1(-5) = (-1)3(-5) = 5


a22 (co – factor of 2) = (-1)2+2(3) = (-1)4(3) = 3



Now, adj A = Transpose of co-factor Matrix



Calculating A (adj A)






= I


Calculating (adj A)A






= I


Calculating |A|.I





= [3 × 2 – (-1) × (-5)]I


= [6 – (5)] I


= (1)I


= I


Thus, A(adj A) = (adj A)A = |A|I = I


A(adj A) = (adj A)A = |A|I


Hence Proved


Ans.


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