Define $L : M \to \mathbb{R}$ where $M$ is the set of all square matrices. If we define $L(A) = \det(A)$, $A \in M$, is $L$ a linear transformation?

Attempt: This is not a linear transformation because $L(A + B) = \det(A+B) \neq \det(A) +\det(B)$. Is this correct? Also, if it is not a linear transformation, then is it possible (in higher math) to find some $A$, other than a $1 \times 1$ matrix for $L$ to be a linear transformation?