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Question:

GivenA=[2𕒷󔼷], computeA𕒵ans show that2A𕒵=9I−A.GivenA=[2𕒷󔼷], computeA𕒵ans show that2A𕒵=9I−A.A=[2𕒷󔼷]A=[2𕒷󔼷]A=[2𕒷󔼷]AA==[2𕒷󔼷][[2𕒷�𕒷��𕒷𕒷−󔼩󔼷𕒸𕒸−�]]A𕒵A𕒵A𕒵A𕒵AAA𕒵𕒵𕒵−�A𕒵=9I−A2A𕒵=9I−A2A𕒵=9I−A22A𕒵AAA𕒵𕒵𕒵−󔼓==99II−−AA?

Solution:

A=[2𕒷󔼷]|A|=14󔼔=2A𕒵=cofactormatrixofA|A|=12[7342]9I−A=[9009]−[2𕒷󔼷]=[7342]=2A𕒵Therefore,2A𕒵=9I−AProved.