Which of the following are correct?

(A) $A=\begin{bmatrix}-9 & 4 & -3\\-1 & 0 & 4\\2 & 2 & 0\end{bmatrix}$ ; $a_{22}+a_{32}=-9$ where $a_{ij}$ denotes the $(i,j)^{th}$ element of matrix A.

(B) $A=\begin{bmatrix}2 & -2\\-2 & 2\end{bmatrix}$; $A^2=pA$, then $p=4$

(C) $\begin{bmatrix}8 & 6\\6 & 16\end{bmatrix}$ is a symmetric matrix

(D) $\begin{bmatrix}0 & -5 & 3\\5 & 0 & -7\\-3 & 7 & 0\end{bmatrix}$ is a symmetric matrix

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If the area of a triangle whose vertices are $(-2, 4)$, $(2, -6)$ and $(k, 4)$, $(k > 0)$ is 35 squnits, then the value of k is

If $\begin{bmatrix} 3 & 2x+5y & -2 \\ x+4y & 7 & -5 \end{bmatrix} = \begin{bmatrix} 3 & 10 & -2 \\ 2 & 7 & -5 \end{bmatrix}$ Then the values of $x$ and $y$ are :

For every square matrix $A$ of order $n\times n$, which of the following statements are correct ?

(A) $(adjA)A = A(adjA) = |A|I$, where $I$ is identity matrix of order n.

(B) $|kA|=k^n|A|$, k is any scalar.

(C) $|adjA|=|A|^n$

(D) $A^2=A$

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If $A$ is a square matrix of order $n \times n$, then which of the following are correct?

(A) $|kA| = k^n|A|$, $k$ is a constant

(B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant

(C) $|adj\ adjA| = |A|^{(n-1)^2}$

(D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$

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If A is a square matrix such that $A^2 = A$ then which of the following statements are TRUE ? (Where I is an identity matrix of same order as A)

(A) $(I+A)^4 = I + 15A$

(B) $(I+A)^2 = I + 3A$

(C) $(I+A)^6 = I + 30A$

(D) $(I+A)^3 = I + 7A$

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If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is