Answer to Question #339475 in Linear Algebra for Mmq

Question #339475

If the characteristic polynomial of a matrix A is p(λ) = λ2+ 1, then A is invertible


1
Expert's answer
2022-05-17T15:08:21-0400

P("\\lambda" )="\\lambda" 2+1"\\implies" "\\exist" A-1

det(A-"\\lambda" E)="\\begin{vmatrix}\n - \\lambda& 1 \\\\\n -1 & - \\lambda\n\\end{vmatrix}"=P("\\lambda" )

"A=\\begin{pmatrix}\n 0 & 1 \\\\\n -1 & 0\n\\end{pmatrix}"

detA=1 don`t equal 0"\\implies\\exist" A-1

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