Cyclobutyl bromide on treatment with magnesium in dry ether forms an organometallic $\left(\mathrm{A}\right)$. The organometallic $\left(\mathrm{A}\right)$ reacts with ethanal to give an alcohol $\left(\mathrm{B}\right)$ after mild acidification. Prolonged treatment of alcohol $\left(\mathrm{B}\right)$ with an equivalent amount of $\mathrm{HBr}$ gives $1-$bromo$-1-$methyl cyclopentane $\left(\mathrm{C}\right)$. Write the structures of $\left(\mathrm{A}\right),\left(\mathrm{B}\right)$ and explain how $\left(\mathrm{C}\right)$ is obtained from $\left(\mathrm{B}\right)$