The sum of a matrix $A$ and its transpose is $\begin{bmatrix}6 & -1\\ -1 & 4\end{bmatrix}$.

Which of the following statements is true?

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$, then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

Let $A = \begin{bmatrix} 2 & -3 & 4 \\ 0 & 1 & 5 \\ -4 & 2 & 3 \end{bmatrix}$ and $a_{ij}$ be any element of matrix A, i, j ∈ {1,2,3}, then which of the following are TRUE?

(A) Minor of $a_{23} = 16$

(B) Minor of $a_{23} = -8$

(C) Cofactor of $a_{23} = -16$

(D) Cofactor of $a_{23} = 8$

(E) Cofactor of $a_{13} = 4$

Choose the correct answer from the options given below:

Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$, $a_{ij}=i+j$, then

Match List-I with List-II

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} 1 & bc & bc(b+c) \\ 1 & ca & ca(c+a) \\ 1 & ab & ab(a+b) \end{vmatrix}$ is

If $A$ is a square matrix such that $A^2 = A$ and $I$ is the identity matrix of the same order as $A$, then $(I + 2A)^2 - 5A$ is equal to

If $A = \begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix}$ and $B^T = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & -1 \end{bmatrix}$, then $A - B$ is equal to