Mathematics - Matrix Question with Solution | TestHub

$A=\left[\begin{array}{cc}5a& -b\\ 3& 2\end{array}\right]$and$A^T=\left[\begin{array}{cc}5a& 3\\ -b& 2\end{array}\right]$

$A{A}^T=\left[\begin{array}{cc}25a^2+b^2& 15a-2b\\ 15a-2b& 13\end{array}\right]$

Now,$A.adjA=\left|A\right|I_2=\left[\begin{array}{cc}10a+3b& 0\\ 0& 10a+3b\end{array}\right]$

Given$A{A}^T=A.adj A$

$15a-2b=0$......(i)

$10a+3b=13$.......(ii)

Solving we get

$5a=2$and$b= 3$

$\therefore$$5a+b=5$