If the matrix $\begin{bmatrix} x & x^2+3x & 5 \\ -2x-6 & x^2 & -4x-2 \\ 5 & x^2+2 & x^3 \end{bmatrix}$ is a symmetric matrix,then the value of $x$ is

In an upper triangular matrix of order $n \times n$,the minimum number of zeros is:

If $A$ and $B$ are square matrices of size $n \times n$ such that $A^2 - B^2 = (A - B)(A + B)$,then which of the following will be always true?

$A$ square matrix $A = [a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

If $A=\left[\begin{array}{rrr}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$,$B=\left[\begin{array}{rr}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ and $C=\left[\begin{array}{rrrr}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right]$,find $A(BC)$,$(AB)C$ and show that $(AB)C=A(BC)$.

Construct a $3 \times 4$ matrix,whose elements are given by $a_{i j}=2 i-j$.