Question

For an invertible nxn matrix A, what is the relationship between det (A) and det (A)?

Short answer

Therefore, the relationship of det (A) and det (A) is given by,

$detadjA={\left(detA\right)}^{n-1}$

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 x n”

To find the relationship of  and

To find the relationship,

We know that,

$adjA=\left(detA\right)A^{-1}$.

Therefore,

$$\begin{gathered} detadjA=det\left(\left(detA\right)A^{-1}\right) \\ detadjA={\left(detA\right)}^{n}det{A}^{-1} \\ detadjA={\left(detA\right)}^{n-1} \end{gathered}$$