Subject Experts Solutions for Chapter: Matrices, Exercise 1: Practice Exercise

Which one of the following matrices is an elementary matrix$?$

The matrix $\left[\begin{array}{cc}0& -4+i\\ 4+i& 0\end{array}\right]$ is

If $X=\left[\begin{array}{ll}3& -4\\ 1& -1\end{array}\right],B=\left[\begin{array}{cc}5& 2\\ -2& 1\end{array}\right]$ and $A=\left[\begin{array}{ll}p& q\\ r& s\end{array}\right]$ satisfy the equation $AX=B$, then the matrix $A$ is equal to

Let $A=\left[\begin{array}{cc}x+y& y\\ 2x& x-y\end{array}\right], B=\left[\begin{array}{c}2\\ -1\end{array}\right]$ and $C=\left[\begin{array}{l}3\\ 2\end{array}\right]$. If $AB=C$, then what is $A^2$ equal to$?$

If $E\left(\theta \right)=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$, then $E\left(\alpha \right)E\left(\beta \right)$ is equal to

If $A=\left[\begin{array}{rrr}1& 0& -2\\ 2& -3& 4\end{array}\right]$, then the matrix $X$ for which $2X+3A=0$  holds true is

If $A=\left[\begin{array}{ccc}1& 1& -1\\ 2& -3& 4\\ 3& -2& 3\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& -2& -1\\ 6& 12& 6\\ 5& 10& 5\end{array}\right]$, then Which of the following is/are correct$?$

$\mathrm{I}$. $A$ and $B$ commute

$\mathrm{II}$. $AB$ is a null matrix. Select the correct answer using the code given below.

Consider the following in respect of the matrix

$A=\left[\begin{array}{cc}-1& 1\\ 1& -1\end{array}\right]$

$\mathrm{I}$. $A^2=-A$

$\mathrm{II}$. $A^3=4A$

Which of the above statement(s) is/are correct?