Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.


Here,

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


a11 (co – factor of 2) = (-1)1+1(9) = (-1)2(9) = 9


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


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


a22 (co – factor of 9) = (-1)2+2(2) = (-1)4(2) = 2



Now, adj A = Transpose of co-factor Matrix



Calculating A (adj A)







= 3I


Calculating (adj A)A







= 3I


Calculating |A|.I





= (2 × 9 – 3 × 5)I


= (18 – 15)I


= 3I


Thus, A(adj A) = (adj A)A = |A|I = 3I


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


Hence Proved


Ans.


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