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If A is an 3xx3 non-singular matrix su...

If A is an `3xx3` non-singular matrix such that `A A^T=A^T A` and `B""=""A^(-1)A^T` , then `BB^T` equals (1) `I""+""B` (2) `I` (3) `B^(-1)` (4) `(B^(-1))^T`

A

`I+B`

B

`I`

C

`B^(-1)`

D

`(B^(-1))'`

Text Solution

Verified by Experts

The correct Answer is:
B
`B=A^(-1) A'`
`implies AB=A'`
`AB B'=A'B'=(BA)'`
`=(A^(-1) A'A)'=(A^(-1) A A')'=A`
`implies B B'=I`
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