Question

The equation $\mathit{d}\mathit{e}\mathit{t}\left(-A\right)\mathbf{=}\mathit{d}\mathit{e}\mathit{t}\mathit{A}$holds for all $\mathbf{6}\mathbf{\times }\mathbf{6}$matrices.

Short answer

Therefore, the given condition is true.

Step-by-step solution

Matrix Definition. 

Matrix is a setof numbers arranged in rows and columns so as to form a rectangular array.

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.

If A is a $6\times 6$matrix,

Then

$\det (-A)=(-1{)}^{6}detA$

$det(-A)=detA$.

Therefore, the given condition is satisfied.