GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/04

Question 04 (Textile Engineering & Fibre Science)

Let $A=\begin{pmatrix} 1 & \frac{1}{2}\\ \frac{1}{2} & 1 \end{pmatrix}$ . The determinant $A^{-1}$ is equal to

(A)	$\frac{1}{2}$
(B)	$\frac{4}{3}$
(C)	$\frac{3}{4}$
(D)	$2$

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$A=\begin{pmatrix} 1 & \frac{1}{2}\\ \frac{1}{2} & 1 \end{pmatrix}$
$A^{-1}=\frac{Adj A}{\left | A \right |}$
$Adj A=\begin{pmatrix} 1 & \frac{-1}{2}\\ \frac{-1}{2} & 1 \end{pmatrix}$
$A^{-1}=\frac{\begin{pmatrix} 1 & \frac{-1}{2}\\ \frac{-1}{2} & 1 \end{pmatrix}}{\left | A \right |}$
$A^{-1}=\frac{\begin{pmatrix} 1 & \frac{-1}{2}\\ \frac{-1}{2} & 1 \end{pmatrix}}{\frac{3}{4}}$
$A^{-1}=\frac{4}{3}$ (Ans)

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