Question

if C is a square matrix that proves this C^2+C=I then prove that C^4=2I-3C

Answer 1

\[C^2+C=I\]\[C^3+C^2=C\]\[C^3+C^2+C=2C\]\[C^3+I=2C\]\[C^4+C=2C^2\]\[C^4+C+2C=2C^2+2C\]\[C^4+3C=2(C^2+C)\]\[C^4+3C=2I\]\[C^4=2I-3C\]

Answer 2

thanks