Amit M Agarwal Solutions for Chapter: Matrix, Exercise 1: Work Book Exercise 1.1

A matrix $A=\left[a_{ij}\right]$ is an upper triangular matrix, if

If $A$ is any $m\times n$ matrix such that $AB$ and $BA$ are both defined, then $B$ is 

If $A=\left[\begin{array}{l}1\\ 2\\ 3\end{array}\right]$ and $B=\left[\begin{array}{ccc}-5& 4& 0\\ 0& 2& -1\\ 1& -3& 2\end{array}\right]$, then

If $A=\left[\begin{array}{rrr}0& c& -b\\ -c& 0& a\\ b& -a& 0\end{array}\right]$ and $B=\left[\begin{array}{lll}{a}^2& ab& ac\\ ab& b^2& bc\\ ac& bc& c^2\end{array}\right]$ then $AB$ is equal to

If $U=\left[\begin{array}{lll}2& -3& 4\end{array}\right],V=\left[\begin{array}{l}3\\ 2\\ 1\end{array}\right],X=\left[\begin{array}{lll}0& 2& 3\end{array}\right]$ and $Y=\left[\begin{array}{l}2\\ 2\\ 4\end{array}\right]$ then the value of $UV+XY$ is

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

Matrix $A$ has $m$ rows and $\left(n+5\right)$ columns, matrix $B$ has $m$ rows and $\left(11-n\right)$ columns. If both $AB$ and $BA$ exist, then

If $A=\left[\begin{array}{cc}1& 0\\ \frac{1}{2}& 1\end{array}\right]$, then $A^{100}$ is equal to