Question

Can Two Different Matrices have the Same Determinant?

Answer 1

Explanation for the correct answer:

Yes,

For example, let us take two different matrices,

$A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]$

Calculate the determinant for these two matrices:

$\left|A\right|=1-0=1$

$\left|B\right|=4-3=1$

Therefore, both the matrices have same determinant value.

Hence, we cay say that, two matrices of different values can have the same value of determinant.