If A and B are invertible matrices of same order, then which of the following is not correct?

For any square matrix \(A\) of order \(n\), the fundamental property relating the matrix and its adjoint is \(A \cdot (\text{adj}A) = (\text{adj}A) \cdot A = |A| I\), where \(I\) is the identity matrix of order \(n\).

Thus, the statement \(A \cdot (\text{adj}A) = (\text{adj}A) \cdot A = A I\) is incorrect.

Since \(A\) and \(B\) are invertible matrices, their determinants must be non-zero, which means \(|A| \neq 0\) and \(|B| \neq 0\).

The reversal law for the inverse of the product of two invertible matrices states that \((AB)^{-1} = B^{-1} A^{-1}\).

Therefore, the only incorrect statement is the first one.

Answer: \(A \cdot (\text{adj}A) = (\text{adj}A) \cdot A = A I\)