Given a matrix A of order 3×3 with ∣A∣=3.
The adjoint of matrix A satisfies the property:
A(adj A)=∣A∣×I
where I is the identity matrix of the same order.
Substituting ∣A∣=3:
A(adj A)=3I
Taking the determinant of both sides:
∣A(adj A)∣=∣3I∣
For a 3×3 identity matrix, when multiplied by scalar k:
∣kI∣=kn×∣I∣
where n is the order of the matrix.
Since the matrix is 3×3:
∣3I∣=33×∣I∣
∣3I∣=33×1
∣3I∣=27
Therefore, ∣A(adj A)∣=27