If $A = \begin{bmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{bmatrix}$, then the matrix (adj A)A is equal to

If $A = [a_{ij}]_{3×3}$ where $a_{ij} = \begin{cases} (-1)^{i+j} - 1, & i = j \\ (-1)^{i+j}, & i \neq j \end{cases}$ then the value of $A + A^T$ is:

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

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If $\begin{vmatrix} 2x & 2 \\ 8 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ 4 & -2 \end{vmatrix}$ then $x =$

Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

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If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = k \cdot a^l b^m c^n$, then

Match List-I with List-II

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If $x,y,z$ are non-zero real numbers such that $\begin{vmatrix} 10+x & 10 & 10 \\ 10 & 10+y & 10 \\ 10 & 10 & 10+z \end{vmatrix}=0$, then the value of $x^{-1}+y^{-1}+z^{-1}$ is