Question

If Ais an invertible $\mathit{n}\mathbf{\times }\mathit{n}$ matrix, then$\mathit{d}\mathit{e}\mathit{t}\left(A^T\right)$ must equal$\mathit{d}\mathit{e}\mathit{t}\mathbf{\left(}{\mathbf{A}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$.

Short answer

Therefore, the given statement is false.

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.

It applies that,

$det{A}^T=detA$

$det{A}^T=\frac{1}{det{A}^{-1}}$, Which is not necessarily equal to $det{A}^{-1}$.

Therefore, the given statement is false.