Identify the compounds $A$ and $B$ in the following reaction.

Identify the product $B$ in the following reaction.
Dry ice $\xrightarrow[\text{dry ether}]{CH_3MgBr} A$ $\xrightarrow{H_3O^{+}} B$

Compare the two methods shown for the preparation of carboxylic acids.
Method $1$: $RBr$ $\xrightarrow[diethyl \ ether]{Mg} RMgBr$ $\xrightarrow[2. \ H_3O^{+}]{1. \ CO_2} RCO_2H$
Method $2$: $RBr$ $\xrightarrow{NaCN} RCN$ $\xrightarrow[heat]{H_2O, HCl} RCO_2H$
Which one of the following statements correctly describes this conversion for the given substrate ($1$-bromoadamantane)?

Which among the following compounds is $NOT$ used for the preparation of aromatic carboxylic acids from alkyl benzene?

What is $A$ in the following reaction?
$Cyclopropyl bromide \xrightarrow[(ii) CO_2, (iii) H_3O^+]{(i) Mg, Et_2O} A$

Give the reaction methods to prepare carboxylic acid from amide compounds.