Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: Level 1

Let the matrix $F\left(x\right)=\left[\begin{array}{ccc}\cos x& -\sin x& 0\\ \sin x& \cos x& 0\\ 0& 0& 0\end{array}\right]$. Then $F\left(x\right)F\left(y\right)=$

The value of  $(x+y)$, where $x$ and $y$ are satisfying $\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{ll}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$ is

Which of the following is not true?

If $A=\left[\begin{array}{ll}1& 0\\ 1& 1\end{array}\right]$, then $A^{2008}$ is equal to

If the square matrices $A$ and $B$ are such that $AB=A$ and $BA=B$, then

If $a,b$ and $c$ are in arithmetic progression, then the value of the determinant $\left|\begin{array}{ccc}x+2& x+3& x+2a\\ x+3& x+4& x+2b\\ x+4& x+5& x+2c\end{array}\right|$ is -

If $x, y$ and $z$ are greater than $1$, then the value of $\left|\begin{array}{ccc}1& {\log }_{x}y& {\log }_{x}z\\ {\log }_{y}x& 1& {\log }_{y}z\\ {\log }_{z}x& {\log }_{z}y& 1\end{array}\right|$ is

A square matrix $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right],$ then which of the following statement is not correct?