Question: For the matrix show that A 2 4A 5I = 0 and hence that A 1 = 1/5 (A 4I). Calculate A

For the matrix

[1 2 2] A = 2 1 2 2 2 1

show that A² – 4A – 5I = 0 and hence that A^–1 = 1/5 (A – 4I). Calculate A^–1 from this result. Further show that the inverse of A² is given by 1/25 (21I – 4A) and evaluate.

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