The value of $\begin{vmatrix}x & a & a\\a & x & a\\a & a & x\end{vmatrix}$ is equal to:

If area of the triangle formed by A(1, 3), B(0, 0) and C(k, 0) is 3 sq. units, then which of the following is/are TRUE?

A. k = 2

B. k = -2

C. k = 3

D. k = -3

Choose the correct answer from the options given below:

Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix}$ and $x, y$ are natural numbers, then the number of solutions for the system is:

If $A$ and $B$ are invertible matrices of order 3. If $|A| = 2$ and $|(AB)^{-1}| = \dfrac{-1}{6}$, then the value of $|B|$ is :

The number of all possible matrices of order 3 with each entry either 0 or 1 is:

If $A$ is a skew-symmetric matrix and $n$ is an odd positive integer, then $A^n$ is :

Which of the following statements are correct ?

A. If the product of 2 non-zero square matrices is a zero matrix, then either A is singular or B is singular

B. If A is a non singular matrix , then $|A^{-1}| = \dfrac{1}{|A|}$

C. If A is an invertible square matrix then $adj\,A^T = \dfrac{1}{adj\,A}$

D. If A and B are invertible matrices then $(AB)^{-1} = B^{-1}A^{-1}$

Choose the correct answer from the options given below: