If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

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 $A=\begin{bmatrix}a & 0 \\ b & 0\end{bmatrix}$ and $A^2=\begin{bmatrix}4 & c \\ 2 & 0\end{bmatrix}$, $a,b,c \in \mathbb{Z}$. Then the minimum value of $a+b+c$ is:

Let A be a non singular square matrix of $2 \times 2$. Then, $|adj\ A|$ is equal to

If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $(A - I)^3 + (A + I)^3 - 3A$ is equal to

Given $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} x & y \\ 1 & 4 \end{bmatrix}$, If $A = B$, then $x$ and $y$ are :

If $A = \begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then $|adj A|$ is equal to