4. In the following, determine whether the statement is true or false, and justify your answer.
a) For all square matrices A and B, it is true that $det(A+B) = det(A) + det(B)$.
b) If A is an $n \times n$ matrix and B is obtained from A by multiplying each row of A by its row
number, then
$$det(B) = \frac{n(n+1)}{2}det(A).$$
c) If the sum of the second and fourth row vectors of a 6 x 6 matrix A is equal to the last
row vector, then $det(A) = 0$.
d) If A has a row of zeros, then so does $adj(A)$.
