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:
Calculating A (adj A)
= 12I
Calculating (adj A)A
= 12I
Calculating |A|.I
Expanding along C1, we get
= [1(3 – 0) – (-1){9 – (-2)} + 2(0 – 1)]I
= [3 + 1(11) + 2(-1)] I
= (3 + 11 – 2 )I
= 12I
Thus, A(adj A) = (adj A)A = |A|I = 12I
⇒ A(adj A) = (adj A)A = |A|I
Hence Proved
Ans.