If , prove that A 3 6A 2 + 7A + 2I = 0 A 3x3 matrix A with elements [[1,0,2],[0,2,1],[2,0,3]].

A2 = A.A Now, A3 = A2. ANow, A3 – 6A2 + 7A + 2I Therefore, A3 – 6A2 + 7A + 2I = 0

Q16 of 108 Page 80

If, prove that A₃ – 6A² + 7A + 2I = 0

A² = A.A

Now, A³ = A². A

Now, A³ – 6A² + 7A + 2I

Therefore, A³ – 6A² + 7A + 2I = 0

Show that

Find A² – 5A + 6I, if

If , find k so that A² = kA – 2I

If and I is the identity matrix of order 2, show that