The correct answer is A. homogeneous of degree 2.
A homogeneous production function is a function that remains unchanged when all inputs are multiplied by the same positive constant. In other words, if $Y=f(K,L)$ is a homogeneous production function of degree $r$, then $Y(tK,tL)=t^rY(K,L)$ for any positive constant $t$.
In the case of the production function $Y=LK$, we have $Y(tK,tL)=t^2LK=t^2Y(K,L)$. Therefore, $Y=LK$ is a homogeneous production function of degree 2.
A homogeneous production function of degree 1 is called a linear production function. A homogeneous production function of degree 0 is called a constant returns to scale production function. A homogeneous production function of degree -1 is called a decreasing returns to scale production function. A homogeneous production function of degree -2 is called an increasing returns to scale production function.
A non-homogeneous production function is a function that is not homogeneous. In other words, if $Y=f(K,L)$ is a non-homogeneous production function, then $Y(tK,tL)\neq t^rY(K,L)$ for some positive constant $t$.