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If A, B are two square matrices of same ...

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

A. `AB=BA`

B

B. `|A-I|=0`

C

C. `|B-I| ne 0`

D

D. `|A-B|=0`

Text Solution

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The correct Answer is:
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
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