Question

State true or false:

The product matrix of $\left[\begin{array}{c}10\\ 01\end{array}\right]$ and $\left[\begin{array}{c}01\\ 10\end{array}\right]$ is an identity matrix.

• A. True
• B. False

Answer 1

The correct option is B False

Consider,

$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\times \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

$=\left[\begin{array}{cc}1\left(0\right)+0\left(1\right)& 1\left(1\right)+0\left(0\right)\\ 0\left(0\right)+1\left(1\right)& 0\left(1\right)+1\left(0\right)\end{array}\right]$

$=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],$ which is not an identify matrix of order $2\times 2$.

Hence given statement is false.