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A and B be 3xx3 matrices such that AB+A+...

`A` and `B` be `3xx3` matrices such that `AB+A+B=0`, then

A

A. `(A+B)^(2)=A^(2)+2AB+B^(2)`

B

B. `|A|=|B|`

C

C. `A^(2)=B^(2)`

D

D. none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Given `AB+A+B=0`
`impliesAB+A+B+I=I`
`impliesA(B+I)+(B+I)=(`
`implies(A+I)(B+I)=I`
`implies (A+I)` and `(B+I)` are inverse of each other
`implies(A+I)(B+I)=(B+I)(A+I)`
`impliesAB=BA`
Thus `A` and `B` are commutative
`implies(A+B)^(2)=A^(2)+2AB+B^(2)`
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