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)
= -132I
Calculating (adj A)A
= -132I
Calculating |A|.I
Expanding along C1, we get
= [4(0 – 42) – (1){45 – 21} + 2(30 – 0 )]I
= [4(-42) – 1(24) + 2(30)] I
= (-168 – 24 + 60)I
= -132I
Thus, A(adj A) = (adj A)A = |A|I = -132I
⇒ A(adj A) = (adj A)A = |A|I
Hence Proved
Ans.