# how to verify that det(A)=det(A^T). For example : A = first row (-2,3) , second row (1,4) ?

Refer to explanation

#### Explanation:

For A=(-2,3;1,4)

the $\det \left(A\right) = \left(- 2\right) \cdot 4 - 3 \cdot 1 = - 8 - 3 = - 11$

For A^T=(-2,1;3,4)

the $\det \left({A}^{T}\right) = \left(- 2\right) \cdot 4 - 3 \cdot 1 = - 11$

hence $\det A = \det {A}^{T}$