Question

There exists a nonzero$\mathbf{4}\mathbf{\times }\mathbf{4}$ matrixAsuch that$\mathit{d}\mathit{e}\mathit{t}\mathit{A}\mathbf{=}\mathit{d}\mathit{e}\mathit{t}\mathit{A}\left(4A\right)$.

Short answer

Therefore, the given condition is true.

Step-by-step solution

Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “ m by n ” matrix, written “$m\times n$ .”

To check whether the given condition is true or false.

For example,

$A=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

Indeed,

$detA=0=det\left(4A\right)$.

Therefore, the given condition is true.