Question

If A$={\left[\begin{array}{cc}0& a\\ b& 0\end{array}\right]}^4=I$

• A. $a=1=2b$
• B. $a=b$
• C. $a=b^2$
• D. $ab=1$

Answer 1

The correct option is D

$ab=1$

Explanation for the correct option:

Given,

$A={\left[\begin{array}{cc}0& a\\ b& 0\end{array}\right]}^4=I$

$\left[\begin{array}{cc}0& a\\ b& 0\end{array}\right]\left[\begin{array}{cc}0& a\\ b& 0\end{array}\right]{\left[\begin{array}{cc}0& a\\ b& 0\end{array}\right]}^2=I$

$\left[\begin{array}{cc}0& {\left(ab\right)}^2\\ {\left(ab\right)}^2& 0\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$$\begin{gathered} {\left(ab\right)}^2=1 \\ \left(ab\right)=1 \end{gathered}$$

Hence, correct option is (D).