7. Find the determinant of the matrix.

$$

C = \begin{bmatrix}

al & J & J & J \\

J & al & J & J \\

J & J & al & J \\

J & J & J & al

\end{bmatrix}

$$

where $a eq 0$ and each matrix has dimension $n \times n$. What are the conditions on

$a$ and $n$ to insure that the inverse exists?