3× 3 matrices are formed using the elements from the set {-3,-2,-1,0,1,2,3} then answer the following. Number of matrices that are skew symmetric matrices (or) scalar matrices is

Let A be a skew symmetric matrix $A\left[\begin{array}{l}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}y\\ -\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}z\\ -\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right]\text{ for }$

x,y,z each can be filled in 7 ways corresponding to each of x,y,z other places can be filled in 1 ways.

$\therefore n\left(A\right)=7^3$

B : Scalar matrix, then n(B) = 7

$n(A\cap B)=1$ (All entries are zeros)

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$=7^3+7.1-1=7^3+6$