Question

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

Answer 1

Answer:

Step-by-step 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, $B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}$