Match List I with List II

Choose the correct answer from the options given below :

A-II, B-IV, C-I, D-III

The correct answer is Option (1) → A-II, B-IV, C-I, D-III

(A) No. of possible matrix is, $2^6=64$

(B) $\begin{bmatrix}5 & 3\\1 & -3\end{bmatrix}$ ⇒ Sum of Diagonal elements = $5+(-3)=2$

(C) $\begin{bmatrix}a-b & 11\\-5 & a^2-b^2\end{bmatrix}=\begin{bmatrix}3&11\\-5&27\end{bmatrix}$ then $\frac{(ab)}{2}$

$⇒a-b=3$  ...(1)

$⇒a^2-b^2=27$   ...(2)

From (1) and (2),

$a+b=9$   ...(3)

Adding (1) and (3),

$2a=12$

$a=6⇒b=3$

$∴\frac{(ab)}{2}=\frac{6×3}{2}=9$

(D) All the diagonal elements of skew symmetric matrices are zero.

∴ Sum = 0