Given that A is a square matrix of order 3×3 and ∣A∣=4.
For any square matrix A:
(adjA)⋅A=∣A∣⋅I
where I is the identity matrix.
Substituting ∣A∣=4:
(adjA)⋅A=4I
where I is the 3×3 identity matrix.
Taking determinant on both sides:
∣(adjA)⋅A∣=∣4I∣
For an n×n identity matrix multiplied by a constant k:
∣kI∣=kn
Since the matrix is 3×3:
∣4I∣=43
∣4I∣=64
Therefore, ∣(adjA)⋅A∣=64