Question

Consider $A$ and $B$ two square matrices of same order. Select the correct alternative

• A. $|A+B|$ must be greater than $|A|$
• B. If $AB=0$ either $A$ or $B$ must be zero matrix
• C. $|AB|$ must be greater than $|A|$
• D. $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$ is not unit matrix

Answer 1

The correct option is D $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$ is not unit matrix

$|A+B|=|A|+|B|$
$|A+B|>|A|$ only when $|B|\ge 0$

$|AB|=|A||B|>|A|$ only when $|B|>1$

Unit matrix
$=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$