If $\begin{bmatrix} ab & cd \\ a+c & b+d \end{bmatrix} = \begin{bmatrix} 2 & -3 \\ 4 & 1 \end{bmatrix}$ where $a$, $b$, $c$, $d$ are integers, then which of the following are true?

(A) $a + d = 0$

(B) $b + d = 3$

(C) $b + d = 1$

(D) $c + d = 2$

Choose the correct answer from the options given below:

If $A = [a_{ij}]_{2×2}$ where $a_{ij} = \begin{cases} 1, & i \neq j \\ 0, & i = j \end{cases}$ and $I$ is the identity matrix of order 2, then $(A^2 - 3A + 4I)$ is

(A) Symmetric Matrix

(B) Skew-symmetric Matrix

(C) Non-singular Matrix

(D) Square Matrix

Choose the correct answer from the options given below:

If $a_{ij}=i+3j$, then the matrix of order 2 with elements as $a_{ij}$ is

Which of the following matrices are invertible?

(A) $\begin{bmatrix} 2 & 2 \\ 3 & 3 \end{bmatrix}$

(B) $\begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}$

(C) $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix}$

(D) $\begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 2 & -2 & 1 \\ 0 & 4 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 & 7 \\ 2 & 0 & 6 \end{bmatrix}$ are two matrices such that $3A - 2B + 4C = 0$, then matrix $C$ is equal to:

The difference of two different skew-symmetric matrices is:

If $a$, $b$ and $c$ are distinct prime numbers then the value of $\begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{vmatrix}$ is equal to