Solution Found!
Let A be an invertible matrix. Show that (An)?l = (A?1) n
Chapter 2, Problem 21E(choose chapter or problem)
QUESTION:
Problem 21E
Let A be an invertible matrix. Show that (An)‒l = (A‒1) n whenever n is a positive integer.
Questions & Answers
QUESTION:
Problem 21E
Let A be an invertible matrix. Show that (An)‒l = (A‒1) n whenever n is a positive integer.
ANSWER:
Solution
In this question we have to prove that .
Step 1
Taking Left hand side (L.H.S)
Put we get ,
=>
Now, taking right hand side (R.H.S)
Put we get ,
=>
So, L.H.S = R.H.S