If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$, then $|A|$ 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:

Which of the following statements are true?

(A) A matrix which is both symmetric as well as skew-symmetric is a null matrix.

(B) All positive integral powers of a symmetric matrix are symmetric.

(C) If A is a square matrix, then $A+A^T$ is a symmetric matrix.

(D) All positive even integral powers of a skew-symmetric matrix are skew-symmetric.

Choose the correct answer from the options given below:

If $XA=(I-A)^2$ where $X, A$ and $I$ are $2\times2$ matrices and $A=\begin{bmatrix}1 & 2\\1 & 4\end{bmatrix}$, then $|X|=$

Let $A$ and $B$ be square matrices of order 3, then det $[(A - A^T) + (B - B^T)]$ 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

Choose the correct answer from the options given below:

The system of equation $2x + \lambda y = 8$, $\lambda x + 8y = 3$

has a unique solution if the value of $\lambda$ is (are):