show that if a square matrix A satisfies the equation

Question

A² + 5A -2I = 0 THEN A^-1 = 0.5 (A + 5I ) . 

Answer 1

A² + 5A -2I = 0

A² + 5A =2I  (multiply both sides from right by A^-1)

 

A*A*A^-1+5AA^-1=2I*A^-1

A*I+5I=2A^-1

A^-1=0.5(A+5I)