Determinant of matrix

Question

What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?

Answer 1

 for a nxn matrix A, and any scalar α, det(αA) = α^n det(A).

so answer is 48

Reference https://www.physicsforums.com/threads/determinant-of-a-matrix-multiplied-by-a-scalar.194725/

Answer 2

Let A=$\begin{bmatrix} A & B &C &D \\ E &F &G &H \\ I& J & K & L\\ M & N & O &P \end{bmatrix}$

$det(A)=\mid A \mid =\begin{vmatrix} A &B &C &D \\ E& F &G &H \\ I & J &K &L \\ M &N &O &P \end{vmatrix}$

$2\mid A \mid =\begin{vmatrix} 2A &2B &2C &2D \\ 2E& 2F &2G &2H \\ 2I & 2J &2K &2L \\ 2M &2N &2O &2P \end{vmatrix}$

Take 2 common from every column

$2\mid A \mid =2\times2\times2\times2\times\begin{vmatrix} A &B &C &D \\ E&F &G &H \\ I & J &K &L \\ M &N &O &P \end{vmatrix}$

$2\mid A \mid =2\times2\times2\times2\times 3$

$2\mid A \mid =48$