Finding out values from Matrix equation

Question

Consider two 3 x 3 matrices A and B satisfying $ A = Adj B - B^T $ and $ B = Adj A - A^T $ (where $ C^T $denotes transpose of matrix $C $)

1) If $A $ is non singular, then $(det A)^2 + (det B)^2 $ is equal to?

2) $AB$ is equal to?

Answer 1

Hint:

If $A$ is an $n \times n$ matrix, then $$\text{det}(\text{Adj}(A))=(\text{det}(A))^{n-1}$$

and

$$\text{det}(A^{T})=\text{det}(A)$$