Question

T F IfA and B are similar matrices, then AT=BT

Answer 1

Explanation:

We know that for two similar matrices
`A` and
`B` exists an invertible matrix
`P` for which

`[tex]B = P^(-1) AP`[/tex]

∴
`B^(T) = (P^(-1))^(T) A^(T) P^(T) \\`

Also
`P^(-1)P = I\\`

and
`(P^(-1))^(T) = (P^(T))^(-1)`

∴
`(P^(-1))^(T)P^(T) = I`

so,
`B^(T) = (P^(-1))^(T) A^(T) P^(T) = (P^(T))^(-1)A^(T) P^(T)\\B^(T) = A^(T) I\\B^(T) = A^(T)`