If $A = \begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then the value of $3x+y-2z$ is

Which of the following statements are correct?

(A) If A is a square matrix, then $|A^2| = |A|^2$.

(B) If A and B are square matrices of the same order, then det (AB) = det (A) + det (B).

(C) If A is a square matrix of order 3 and $|A|=2$, then the value of $|-3A|$ is 54.

(D) If the matrix $\begin{bmatrix} 5 -x & x -1 \\ 3 &5 \end{bmatrix}$ is singular, then the value of x is 7/2.

Choose the correct answer from the options given below:

Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$

(D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$

Choose the correct answer from the options given below:

The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively:

The value of the determinant $\begin{vmatrix} a\cos\theta & b\sin\theta & 0 \\ -b\sin\theta & a\cos\theta & 0 \\ 0 & 0 & c \end{vmatrix}$ is :

If the points (a, b), (c, d) and (a + c, b + d) are collinear, then

If $\begin{vmatrix} x-2 & -3 \\ 3x & 2x \end{vmatrix} = 3$, then the values of $x$ are: