Let A = [ 1221].(a) Show that A2 2A + 5I = O, where I is theidentity matrix of order
Chapter 2, Problem 76(choose chapter or problem)
Let A = \(A=\left[\begin{array}{rr} 1 & 2 \\ -2 & 1 \end{array}\right] \).
a) Show that \(A^{2} − 2A + 5I = O\), where I is the identity matrix of order 2.
(b) Show that \(A^{−1} = \frac {1}{5} (2I − A)\).
(c) Show that for any square matrix satisfying (A^{2} − 2A + 5I = O\), the inverse of A is \(A^{−1} = \frac {1}{5} (2I − A)\).
Text Transcription:
A = [_-2^1 _1^2]
A^2 - 2A + 5I = O
A^-1 = 1/5 (2I - A)
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