3 years ago

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

Mathematics

1 answer:

muminat3 years ago

7 0

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

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