How do i increase the input impedance of an inverting amplifier constructed using an op-amp?
Buffer then invert (two amplifiers). The first amplifier (a bootstrapped follower) provides high input impedance, the second provides inversion or inverting gain. 

If you feedback from an inverting amplifier to the input you will lower the input impedance. In the extreme, this is what a transimpedance amplifier does- the input is a virtual ground, so (ideally) 0\$\Omega\$ input impedance. 

You could also try to bootstrap some analog of the input voltage from the output of the inverting amplifier (invert it again, and reverse the gain) but chances are that would not work too well (it would have poor performance or oscillate) because of the multiple stages. This kind of thing is done sometimes to actively drive shields (guards) to the common mode voltage on differential-input amplifiers.