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If A and B are square matrices of order `n ,` then prove that `Aa n dB` will commute iff `A-lambdaIa n dB-lambdaI` commute for every scalar `lambdadot`

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Given, `(A-lambda I)(B-lambda I)=(B-lambda I)(A-lambda I)`

`Rightarrow A B-lambda A-lambda B+lambda^{2}=B A-lambda A-lambda B+lambda^{2}`

`Rightarrow {AB}={BA}`

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