question_answer 52)

For the matrix  show that             A3 ? 6A2 + 5A + 11I = 0. Hence find A?1.  

Answer:

A2 =A.A.                                     A3 = A2 . A                                                                                                       Pre-multiply it by A?1.       A?1 (A3) ? 6A?1 (A2) + 5A?1 (A) 11A?1I = A?1(0)