Question

How can I show that the determinant of matrix A is the same as the determinant of the transpose of matrix A?

Answer 1

\[\left(
\begin{array}{cc}
a & b \\
c & d
\end{array}
\right)\]


ad-bc

\[

\left(
\begin{array}{cc}
a & c \\
b & d
\end{array}
\right)\]

ad-cb

Answer 2

thanks but how can I show this fact for n-order of matrices?

Answer 3

Induction...

Answer 4

thanks.