If the matrix $\begin{bmatrix} 0 & 1 & 4x\ \\ -1 & 0 & -5 \\ 2 & 5 & y \end{bmatrix}$ is skew-symmetric, then

Let the matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$ and $AB = \begin{bmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}$ then order of B is :

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 three points $A(a_1, b_1), B(a_2, b_2)$ and $C(a_3, b_3)$ are collinear and $D = \begin{vmatrix} a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ a_3 & b_3 & 1 \end{vmatrix}$, then:

If $x, y$ & $z$ are non zero real numbers, the inverse of matrix $A = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}$ is :

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

If $a_{ij}$ and $A_{ij}$ represents the elements and cofactors of the matrix $A = \begin{bmatrix}2 & 1 & 3\\3 & 2 & 1\\1 & 2 & 3\end{bmatrix}$, then which of the following statements are True?

(A) $|A| = 28$

(B) $A_{23} = -3$

(C) $a_{11}A_{12} = -16$

(D) $\frac{A_{21}}{A_{13}} = \frac{3}{4}$

Choose the correct answer from the options given below: