QJEEM16Ma34f0: JEE Main 2016 Mathematics - Class 12 JEEM16Ma34f0 Solution: If A = [ 5 a − b 3 2 ] and adj then is equal to :

Question

Verified Solution • 2025–26 Session moderate

If

A = [\begin{matrix} 5 a & - b \\ 3 & 2 \end{matrix}]

and

A

adj

A=A

{A^T},

then

5a+b

is equal to :

Accepted Answer

A\left( {Adj\,\,A} \right) = A\,{A^T}

\Rightarrow {A^{ - 1}}A\left( {adj\,\,A} \right) = {A^{ - 1}}A\,{A^T}

Adj\,\,A = {A^T}

\Rightarrow [\begin{matrix} 2 & b \\ - 3 & 5 a \end{matrix}] = [\begin{matrix} 5 a & 3 \\ - b & 2 \end{matrix}]

\Rightarrow a = {2 \over 5}\,\,

and

\,\,b = 3

\Rightarrow 5a + b = 5

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