# If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A \cdot A^{T}$ then $5 a+b$

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

by (20.7k points)

5a=2
b=3

Now,
5a+b=2+3=5