If two rows of a matrix are equal, its determinant is zero : $$\left|\begin{array}{ccc}a_{11}& a_{12}&a_{13}\\ a_{21}& a_{22}&a_{23}\\a_{21}& a_{22}&a_{23}\end{array}\right|=0$$
Proof
Suppose that \(i\)-th and \(j\)-th rows of a matrix A are equal :
$$A:=\left|\begin{array}{cccc}a_{11}& a_{12}&\cdots &a_{1n}\\\vdots &\vdots &\vdots& \vdots\\a_{i1}& a_{i2}&\cdots &a_{in}\\\vdots &\vdots &\vdots& \vdots\\a_{j1}& a_{j2}&\cdots &a_{jn}\\\vdots &\vdots &\vdots& \vdots\\a_{n1}& a_{n2}&\cdots&a_{nn}\end{array}\right|=\left|\begin{array}{cccc}a_{11}& a_{12}&\cdots &a_{1n}\\\vdots &\vdots &\vdots& \vdots\\a_{i1}& a_{i2}&\cdots &a_{in}\\\vdots &\vdots &\vdots& \vdots\\a_{i1}& a_{i2}&\cdots &a_{in}\\\vdots &\vdots &\vdots& \vdots\\a_{n1}& a_{n2}&\cdots&a_{nn}\end{array}\right|$$
Then, by the property of determinant (3), if \(i\)-th row and \(j\)-th row are interchanged, we have
$$|A|=-|A|$$
Therefore, we obtain
$$2|A|=0$$
and we have proven
$$|A|=0$$