Let A,B, and C be square invertible matrices of the same size. If C has no eigenvalue equal to -1, then (AB + ACB)^-1 is equal t
o:
a. B^-1 (I + C)^-1*A^-1
b. (I + C)^-1*B^-1*A^-1
c. A^-1B*(I + C)^-1
d. (I + C)^-1*BA^-1
1 answer:
<em>AB</em> + <em>ACB</em> = <em>A</em> (<em>B</em> + <em>CB</em>) = <em>A</em> (<em>I</em> + <em>C </em>) <em>B</em>
Taking the inverse gives
(<em>A</em> (<em>I</em> + <em>C </em>) <em>B</em>)⁻¹ = <em>B </em>⁻¹ (<em>I</em> + <em>C</em> )⁻¹ <em>A</em> ⁻¹
so the answer is (A)
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