Matrices

Which one of the following matrices is an elementary matrix?

What is the order of

If $A$ and $B$ are two matrices such that $A B$ is of order $n \times$ $n$, then which one of the following is correct?

If $X$ is a matrix of order $3 \times 3, Y$ is a matrix of order $2 \times 3$ and $Z$ is a matrix of order $3 \times 2$, then which of the following are correct? $(Z Y) X$ is a square matrix having 9 entries. $Y(X Z)$…

If $A, B$ and $C$ are square matrices of order 3 and $\operatorname{det}(\mathrm{BC})$ $=2 \operatorname{det}(\mathrm{~A})$, then what is the value of $\operatorname{det}\left(2 \mathrm{~A}^{-1} \mathrm{BC}\right)$ ?

Consider the following statements in respect of two non-singular matrices A and B of the same order $n$ : $\operatorname{adj}(\mathrm{AB})=(\operatorname{adj} \mathrm{A})(\operatorname{adjB})$…

If $A = \begin{pmatrix} y & z & x \\ z & x & y \\ x & y & z \end{pmatrix}$ where $x$, $y$, $z$ are integers, is an orthogonal matrix, then what is the value of $x^2 + y^2 + z^2$?

If $M_k=\begin{bmatrix} k & k-1 \\ k-1 & k \end{bmatrix}$ where $k$ is a natural number, then what is $|M_1|+|M_2|+|M_3|+\ldots+|M_{50}|$ equal to ?

Paragraph: Let $A=\left(\begin{array}{ccc}0 & \sin ^2 \theta & \cos ^2 \theta \\ \cos ^2 \theta & 0 & \sin ^2 \theta \\ \sin ^2 \theta & \cos ^2 \theta & 0\end{array}\right)$ and $A=P+Q$ where $P$ is symmetric matrix…

Let X be a matrix of order $3 \times 3, \mathrm{Y}$ be a matrix of order $2 \times 3$ and Z be a matrix of order $3 \times 2$. Which of the following statements are correct? A. $(\mathrm{ZY}) \mathrm{X}$ is defined and…

If $[x \ 1 \ 1] \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \begin{pmatrix} 1 \\ 1 \\ x \end{pmatrix} = [45]$, then which one of the following is a value of $x$?

If $A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{pmatrix}$, then what is $A^2 - 4A$ equal to?