If \alpha and \beta are transformations on a set S, prove that \alpha^{



Answered question


If αandβ are transformations on a set S, prove that α1β1 and β1α1 are transformations. Which is the inverse of αβ ? Prove your answer.

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-10-29Added 109 answers

Step 1
Linear transformation are represented as the matrix .
If A and B are two matrix then (AB)1=B1A1or,(B1A1)(AB)1=I
Let us prove the (αβ)1=β1α1
Let us consider sS
Show that
Step 2
Hence proved

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