Question

Anyone understand question 42 in section 2.5 ? Don't know why I am testing inverses to begin with, and have no idea how to manipulate (multiply thru) a whole line of matrices. Do I keep them in the order they appear?

Answer 1

Since \[AC=I\]statement 2I in the book implies that \[CA=I\]Right-multiplying both sides of this equation by C^* gives:\[(CA)C^* = C^*\]Using the associativity of matrix multiplication this means that\[C(AC^*) = C^*\]Since the question states that\[AC^*=I\]we find that \[C=C^*\]as required.