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

Question

Philoid · Accepted Answer

Here,

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

Calculating A (adj A)

=-70 I

Calculating (adj A)A

= -70 I

Calculating |A|.I

Expanding along C₁, we get

= [9(-2 – 32) – (5){14 – 24} + 6(28 – (-3))]I

= [9(-34) – 5(-10) + 6(31)] I

= (-306 + 50 + 186)I

=-70 I

Thus, A(adj A) = (adj A)A = |A|I = -70 I

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.