Prove If $A^{2014}$ is invertible, then $A$ is also invertible Use the associativity of matrix multiplication to prove that if $A^{2014}$ is invertible, then $A$ is also invertible.
Any help please?

As help, consider $AB$ invertible, which means we can find $C$ with $(AB)C=I$ then can you use associativity to show $A$ is invertible? If $B=A$ what does this mean? Can you see how you could apply this to your problem by choosing $B$ appropriately? 
