If `A=[(2,-1),( 3,-2)]`
, then `A^n=`
`[(1, 0),( 0 ,1)]`
, if `n`
is an even natural number
(b) `[(1, 0),( 0, 1)]`
, if `n`
is an odd natural
number
(c) `[-1 ,0 ),(0 ,1)]`
, if `n in N`
(d) none of these
Text Solution
AI Generated Solution
To solve the problem, we need to find the powers of the matrix \( A \) and determine the conditions under which \( A^n \) equals the identity matrix \( I \).
Given:
\[ A = \begin{pmatrix} 2 & -1 \\ 3 & -2 \end{pmatrix} \]
### Step 1: Calculate \( A^2 \)
To find \( A^2 \), we multiply \( A \) by itself:
...
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