Show, that MM-1 = I, where U E Rnxm V E Rmxn a) M=I-uv and M-1 =If uv 1-VT u' b) M = A - uv and M-1 = A-ly A luv Al 1-VIA-lu c) M=I- UV and M-1 = In + U(Im - VU)-IV, d) M= A-UW-IV and M-1 =A-'+A 'U(W-VA-'U)-'VA-1. The last one in the sequence is known as the Sherman-Woodbury- Morrison matrix identity. Notice: These are indeed formulae for the inverse. They should be con- sidered as theoretical constructions and hence, in applications the in- verses within the expressions should be interpreted as solutions of li- near systems of equations