Assertion (A) is true because the metal-carbon bond in metal carbonyls possesses both $\sigma$ and $\pi$ character. Reason (R) is false because the ligand to metal bond is a $\sigma$ bond (formed by the donation of a lone pair of electrons on the carbonyl carbon into a vacant orbital of the metal) and the metal to ligand bond is a $\pi$ bond (formed by the donation of a pair of electrons from a filled $d$ orbital of the metal into the vacant antibonding $\pi^*$ orbital of carbon monoxide).