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If A and B are two matrices such that AB...

If A and B are two matrices such that AB=B and BA=A , then `A^2+B^2=`

A

`A^(2)+B^(2)`

B

`O`

C

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

D

`A+B`

Text Solution

Verified by Experts

As `B=-A^(-1)BA`, we get
`AB=-BA` or `AB+BA=O`
Now,
`(A+B)^(2)=(A+B) (A+B)`
`=A^(@)+BA+BA+B^(2)`
`=A^(2)+O+B^(2)`
`=A^(2)+B^(2)`
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