Question 87107
Any matrix multiplied by its inverse is equal to the identity matrix, I by definition. So:


{{{ (I-A)^(-1)(I-A) = I }}}


Post multiply both sides by (I+A):
{{{ (I-A)^(-1)(I-A)(I+A) = I(I+A) }}}


now, {{{ (I-A)(I+A) = I^2 + IA - AI - A^2 }}}
{{{ (I-A)(I+A) = I^2 + IA - IA - A^2 }}}
{{{ (I-A)(I+A) = I + IA - IA - A^2 }}}
{{{ (I-A)(I+A) = I - A^2 }}}
{{{ (I-A)(I+A) = I }}}


So, {{{ (I-A)^(-1)(I-A)(I+A) = I(I+A) }}} becomes
{{{ (I-A)^(-1) = I(I+A) }}}


and hence {{{ (I-A)^(-1) = (I+A) }}}


cheers
Jon