Let A=122212221, then (A) A2-4A-5I3=0 (B) A-1=15A-4I3 - Maths - Matrices

Question

Let A = 1 2 2 2 1 2 2 2 1 , then
(A) A 2 - 4 A - 5 I 3 = 0 (B) A - 1 = 1 5 A - 4 I 3 (C) A
3 is not invertible (D) A 2 is
invertible

Ashish Shukla · Accepted Answer

Dear Student,
 A=122212221A2=122212221×122212221=988898889Hence, the matrix A2  is invertable, ie
 we can change the rown with the colum and hte matrix do not change
Option D is correct

Let A = 1 2 2 2 1 2 2 2 1 , then (A) A 2 - 4 A - 5 I 3 = 0 (B) A - 1 = 1 5 A - 4 I 3 (C) A 3 is not invertible (D) A 2 is invertible

Let $A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix}]$ , then
(A) $A^{2} - 4 A - 5 I_{3} = 0$ (B) $A^{- 1} = \frac{1}{5} (A - 4 I_{3})$ (C) A ³ is not invertible (D) A ² is invertible