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

1 Answer

Konstantinos Michailidis

Sep 15, 2015

Refer to explanation

Explanation:

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

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

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

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

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

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