Question

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

• A. 5
• B. 4
• C. 13
• D. -1

Answer 1

The correct option is A

5

$A-adjA=|A|=A.A^T\Rightarrow adjA=A^T\left[\begin{array}{cc}2& b\\ -3& 5a\end{array}\right]=\left[\begin{array}{cc}5a& 3\\ -b& 2\end{array}\right]\Rightarrow 5a=2,b=3So,5a+b=5$