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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29