Answer
False
Work Step by Step
Let's analyse these matrixes to see whether the statement is true.
$A=\begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix}$
$B=\begin{bmatrix}
4 & 5 \\
5 & 6
\end{bmatrix}$
$AB=\begin{bmatrix}
14 & 17 \\
32 & 39
\end{bmatrix}$
$adj (AB)=\begin{bmatrix}
39 & -17 \\
-32 & 14
\end{bmatrix}$
$adj (A)=\begin{bmatrix}
4 & -2 \\
-3 & 1
\end{bmatrix}$
$adj (B)=\begin{bmatrix}
6 & -5 \\
-5 & 4
\end{bmatrix}$
$adj (A) adj (B)=\begin{bmatrix}
34 & -28 \\
-23 & 19
\end{bmatrix}$
It is clearly that:
$adj (A) . adj (B) \ne adj (AB)$
Thus, the statement is false.
