Question

. If det.A=5 where A is a square matrix of order 3, then det(adj A) = *

a) 5

B) 25

C) 125

d) 1/5


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Answer 1

Given info : det(A) = 5 where A is square matrix of order 3.

To find : the value of det(adj(A))

Solution : let's derive the formula,

We know, inverse of A = adj(A)/det(A)

⇒A¯¹ = adj(A)/det(A)

⇒det(A) = A adj(A)

⇒det(det(A)) = det(A adj(A))

⇒det(A)ⁿ = det(A) det(adj(A)) , where n is order of matrix A.

⇒det(adj(A)) = det(A)ⁿ¯¹ , this is required formula.

Here, det(A) = 5, n = 3

So, det(adj(A)) = (5)³¯¹ = 5² = 25

Therefore correct option is (B) 25