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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`

A

`AB=BA`

B

`AB+BA=O`

C

`A=-B`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(A-lambda I) (B-lambda I)=(B-lambda I) (A-lambda I)`
or `AB-lambda(A+B)I+lambda^(2)I^(2)=BA-lambda(B+A)I+lambda^(2)I^(2)`
or `AB=BA`
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