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

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?

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 $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$, then$A^2+B^2$ is equal to

Which of the following about the trace of a matrix is false?

Which of the following is not true?

If $a,b,c$  are positive and unequal, the following determinant would be:

$\Delta =\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|$

If $x+ay+a^{2}z=0$,  $x+by+b^{2}z=0$, $x+cy+c^{2}z=0$ ,  $a\ne b\ne c$,  then given system of equations -