If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is

Which of the following statement('s) is/are TRUE?

(A) Skew symmetric matrix of even order is always symmetric

(B) Skew symmetric matrix of odd order is non-singular

(C) Skew symmetric matrix of odd order is singular

(D) Skew symmetric matrix is always square matrix

Choose the correct answer from the options given below:

For $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ where $a, b, c$ are roots of equation $x^3 + px + q = 0$, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

For any 3 ×3 matrix $A$, if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $2|A|$ is equal to

If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If A and B are invertible matrices of same order, then which one of the following is NOT true?