A= [6 5] [7 6] SHOW that A2 - 12A + I = 0 FIND A INVERSE - Maths - Matrices

Question

A= [6 5] [7 6] SHOW that A2 - 12A + I = 0 FIND A INVERSE

Manbar Singh · Accepted Answer

We have,A = 6576so,A2 = 6576 6576 =
6×6+5×76×5+5×67×6+6×77×5+6×6
= 71608471
Now,-12 A = -12 6576 = -72-60-84-72
now, I = 1001now,A2 - 12A + I = A2 + -12A + I=71608471 +
-72-60-84-72 + 1001= 71-72+160-60+084-84+071-72+1 = 0000 = 0so, A2
- 12A + I =0Taking A-1 both side we get, ⇒A-1AA - 12A-1A +
A-1I = 0⇒IA - 12I + A-1 = 0⇒A - 12I + A-1 = 0⇒
A-1 = 12I - A = 120012 - 6576 = 6-5-76