Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 2: Level 2

If $A=\left[\begin{array}{lll}1& 0& 0\\ x& 1& 0\\ x& x& 1\end{array}\right]$ and $I=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ then $A^3-3A^2+3A+I$ is equal to

Let $A=\left[\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right]$ and $B=A+A^2+A^4+A^8+....+A^{2^{78}}$ then sum of all the elements of matrix $B$ is equal to

If  $A$ is a non singular square matrix where $B\mathit{=}{A}^{\mathit{T}}$ & $A\mathit{+}{B}^2=I$, such that $A^3+I\mathit{=}kA$ then $k$is equal to

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

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?

The equation $\left|\begin{array}{ccc}1& x& x^2\\ x^2& 1& x\\ x& x^2& 1\end{array}\right|=0$ has

$\text{ The value of }\left|\begin{array}{ccc}b+c& a& a\\ b& c+a& b\\ c& c& a+b\end{array}\right|\text{ is }$

The system of linear equations $x+y+z=2$, $3x-y+2z=6$ and $3x+y+z=-18$ has