If A is a square matrix of order 3 with $|A| = 4$, then the value of $|2\,adj\,A|$ is:

If A is a square matrix such that $A^2=A$ and I is the identify matrix of the same order as A then $(I + 2A)^3$-6A is equal to

If $\Delta$ represents the value of the determinant $\begin{vmatrix} 1 & \sin k\theta & 1 \\ -\sin k\theta & 1 & \sin k\theta \\ -1 & -\sin k\theta & 1 \end{vmatrix}$, where $k$ is any real number then the value of $\Delta$ belongs to

If $A=\begin{bmatrix}5 & 0 & 0\\0 & 5 & 0\\0 & 0 & 5\end{bmatrix}$ such that $A^5=\lambda^2 A$, then the value of $\lambda$ is

Area of the rectangular plot is:

Match List I with List II: Given that A and B are invertible matrices of size $3 \times 3$

Choose the correct answer from the options given below:

If $A = [a_{ij}]_{3 \times 3}$ and $a_{ij} = i - j$, then which of the following statements are TRUE?

(A). $A$ is scalar matrix

(B). $A$ is skew symmetric matrix

(C). $|A| = 0$

(D). $a_{21} + a_{12} = 0$

Choose the correct answer from the options given below: