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:

If $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 3 & 0 \\ 4 & -8 \end{vmatrix}$, then value(s) of x is/are

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:

Let $A=\begin{bmatrix}a & 0 \\ b & 0\end{bmatrix}$ and $A^2=\begin{bmatrix}4 & c \\ 2 & 0\end{bmatrix}$, $a,b,c \in \mathbb{Z}$. Then the minimum value of $a+b+c$ is:

The value of $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix}$ is:

Let A, B be square matrices of order $3\times3$. Then $|A.adj(A).B|$ is

Let A = PQ. The elementary operation on A, that produces the same effect as it does on applying on P and keeping Q unchanged is :

(A) $R_i \leftrightarrow R_j$

(B) $R_i \to R_i + KR_j$

(C) $C_i \to KC_i$

(D) $C_i \to C_i + KC_j$

Choose the correct answer from the options given below :