Question

If Ais any n x n matrix, then$\mathit{d}\mathit{e}\mathit{t}\left(A{A}^T\right)\mathbf{=}\mathit{d}\mathit{e}\mathit{t}\left(A^{T}A\right)$.

Short answer

Therefore, the given condition is true.

Step-by-step solution

Matrix Definition. 

Matrix is a set 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. 

It applies,

$$\begin{gathered} det\left(A{A}^T\right)=detAdet{A}^T \\ =detAdetA\left(\therefore detA=det{A}^T\right) \\ =det{A}^{T}detA \\ \Rightarrow det\left(A{A}^T\right)=det\left(A^{T}A\right) \end{gathered}$$

Therefore, the given condition is true .