If $A=\begin{bmatrix}\lambda & 0 & 0\\0 & \lambda & 0\\0 & 0 & \lambda\end{bmatrix}$, $\lambda\ne0$, then $|adjA|$ is equal to

The value of $\begin{vmatrix} \log_3 512 & \log_4 3 \\ \log_3 8 & \log_4 9 \end{vmatrix}$ is:

If $A = \begin{bmatrix}1 & -1\\2 & -1\end{bmatrix}, B = \begin{bmatrix}x & 1\\y & -1\end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then which of the following are correct?

A. $x=1$

B. $x=4$

C. $y=1$

D. $y=4$

Choose the correct answer from the options given below:

If A and B are two square matrices of the same order such that $(A+B)^2 = A^2+B^2$, then

Given a matrix A of order 3x3. If |A|=3 then the value of |A(adj A)| is:

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ is

If $A = \begin{bmatrix} 2x & 0 \\ x & x \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1 & 0 \\ -1 & 2 \end{bmatrix}$, then the value of $x$ is