Embibe Experts Solutions for Exercise 5: Assignment

If $A$ is a nilpotent matrix of odd order $r$, then which of the following is true?

The correct statement about the matrix $A=\left[\begin{array}{ccc}1& 4& 5\\ \lambda & 8& 8\lambda -6\\ 1+{\lambda }^2& 8\lambda +4& 2\lambda +21\end{array}\right]$ is/are

If $A$ and $B$ are two $3\times 3$ diagonal matrices, then

Let $A,B$ and $C$ be $2\times 2$ matrices with entries from the set of real numbers.Define $\oplus$ as follows $A\oplus B=\frac{1}{2}\left(AB+BA\right),$ then 

Let, $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right]$ and $\mathrm{I}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ then

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

Which of the following statements are true?

If $abc=\lambda$ and $A=\left[\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right],$where $A$ is orthogonal matrix then