$\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}$ is equal to:

If $\begin{vmatrix}x-2 & 2x-3 & 3x-4\\x-4 & 2x-9 & 3x-16\\x-8 & 2x-27 & 3x-64\end{vmatrix} = 0$ then the value of x is:

If A and B are square matrices of same order n, then identify correct statements from the statements given below:

A. $|adj\ A| = |A|^{n-1}$

B. $|A \cdot B| = |B| \cdot |A|$

C. $adj\ A' = (adj\ A)'$

D. $adj\ AB = (adj\ A) \cdot (adj\ B)$

E. $|A^n| = |A|^n$

Choose the correct answer from the options given below:

Let $A = \begin{bmatrix} 152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0 \end{bmatrix}$. If $A_{ij}$ denotes the co-factor of an element $a_{ij}$ of the matrix A, then the value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ is equal to

If $\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = \det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix}$, then the value of $x$ is

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$)

Let $A$ and $B$ are square matrices of order 3 such that $A + B = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}$. If $A$ is a symmetric matrix, then the value of $|B|$ is