Given that A is a non-singular square matrix of order 3 and ∣adjA∣=5.
For any square matrix of order n, the relationship between the determinant of a matrix and its adjoint is:
∣adjA∣=∣A∣n−1
Since A is of order 3, we have n=3.
∣adjA∣=∣A∣3−1
∣adjA∣=∣A∣2
Substituting the given value ∣adjA∣=5:
5=∣A∣2
∣A∣2=5
∣A∣=±5
Therefore, ∣A∣=±5