Let $A = \begin{bmatrix} 2 & 4 \\ -2 & 8 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$, $\alpha,\beta \in R$ (Where R is set of real numbers) and I is a $2\times2$ identity matrix, than the value of $4(\alpha-2\beta)$ is equal to:

Let $A=[a_{ij}]_{3\times3}$, where $a_{ij}=i-j$, then which of the following statements is/are TRUE ?

A. A is diagonal matrix

B. A is square matrix

C. A is symmetric matrix

D. A is skew symmetric matrix

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If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

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If $x \neq y \neq z$ then $\begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{vmatrix}$ is equal to

If a matrix has 8 elements then the possible order(s) it may have

(A) $8 \times 1$

(B) $5 \times 3$

(C) $6 \times 2$

(D) $2 \times 4$

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If $\begin{bmatrix} x+y & 4 \\ 1+z & y \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 5 & 6 \end{bmatrix}$, then

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 :