If `A`, `B` are two square matrices of same order such that `A+B=AB` and `I` is identity matrix of order same as that of `A`,`B` , then

Question

If `A`, `B` are two square matrices of same order such that `A+B=AB` and `I` is identity matrix of order same as that of `A`,`B` , then

If `A`, `B` are two square matrices of same order such that `A+B=AB` and `I` is identity matrix of order same as that of `A`,`B` , then
A. `AB=BA`
B. `|A-I|=0`
C. `|B-I| ne 0`
D. `|A-B|=0`

Monjur Alahi

5 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::C
`(a,c)` `A+B=AB`
`impliesI-(A+B-AB)=I`
`implies(I-A)(I-B)=I`
`implies|I-A||I-B|=I`
`implies |I-A|`, `|I-B|` are non zero
Also `(I-B)(I-A)=I`
`impliesI-B-A+BA=I`
`impliesA+B=B+A`
`impliesAB=BA`
`implies(a)` and `(c )` are correct

5 views Answered 2023-02-05 15:29