If B is a symmetric matrix and C is a skew symmetric matrix of the same order such that B + C = A then C =

A

$$\frac{1}{2}(A + A^T)$$

B

$$\frac{1}{2}(A^T - A)$$

C

$$\frac{1}{2}(A - A^T)$$

D

$$\frac{1}{2}A A^T$$