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if $A = [\begin{matrix} 5 a & - b \\ 3 & 2 \end{matrix}]$ and Aadj $A = A A^{T}$ Then $5 a + b =$

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Correct option is B

A( adjA)=|A|I where |A|=10a+3b∴AadjA=AAT⇒(10a+3b)1001=5a-b325a3-b2⇒10a+3b0010a+3b=25a2+b215a-2b15a-2b13⇒15a-2b=0 and 10a+3b=13→(1)⇒b=152a→(2)solving the equations then a=25,b=3⇒5a+b=5

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if A=5a−b32and Aadj A=AAT Then5a+b=

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if $A = [\begin{matrix} 5 a & - b \\ 3 & 2 \end{matrix}]$ and Aadj $A = A A^{T}$ Then $5 a + b =$