Today I heard in a lecture (some video on YouTube) that the determinant is linear as a function of each of the rows of the matrix.
I am not able to understand the above statement. I know that determinant is a special function which assign to each $x$ in $\mathbb K^{n \times n}$ a scalar. This is the intuitive idea. And this map is not linear as well. One way to see this is to consider the fact that determinant of $cA$ is $c^n\det(A)$
Can someone please explain what did the person mean by saying that the determinant is linear as a function of each of the rows of matrix?