kI & A & \ldots & A & A\\
A & kI & \ldots & A & A\\
\vdots & & & \vdots & \vdots\\
A & A & \ldots & A & kI
$M$ is a square matrix
That is, $M$ has the $kI$ matrix along its main diagonal and matrix $A$ elsewhere.
$A$ is a matrix of dimension $n\times n$ having all elements equal, $kI$ is also an $n\times n$ matrix, the identity matrix multiplied by a constant $k$
How can I find the determinant efficiently of such matrices for small values of $n$? Can it be done by simple transformations??