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Matrix Determinants Calculator

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Basic Information

Definition: The determinant of the square matrix A=[aij], denoted by det(A) or |A|, is defined as:

|a11a12…a1na21a22…a2n⋮⋮⋱⋮an1an2…ann|= a11|a22a23…a2na32a33…a2n⋮⋮⋱⋮an2an3…ann|−
a12|a21a23…a2na31a33…a2n⋮⋮⋱⋮an1an3…ann|+ ⋯± a1n|a21a22…a2(n−1)a31a32…a3(n−1)⋮⋮⋱⋮an1an2…an(n−1)|
Here are a few theorems that may facilitate calculations of matrix determinants. Let A be a square matrix :
a) The determinant of A and the determinant of its transpose are the same det(A)=det(AT);
b) If A has a row or column of zeros, then det(A)=0;
c) If A has two identical rows (or columns), then det(A)=0;
d) det(AB)=det(A)det(B).
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