00:01
In this question we are given that if matrix a and b are orthogonal.
00:04
So a is given to be orthogonal.
00:07
So this gives us what orthogonal.
00:10
So this gives us that by definition a transpose a is identity which is equivalent to aa transpose or you can also write a inverse is equivalent to a transpose.
00:23
Similarly, we are given b is orthogonal b is orthogonal.
00:28
So this will give us the result that b transpose b is identity, which is equivalent to b times of b transpose or we can also write that b inverse is equivalent to b transpose.
00:41
Now for the first part of the question, we have to show a transpose is orthogonal.
00:45
Now to prove for a transpose what we have to do we have to prove if i substitute a transpose is in place of a this will become a transpose transpose multiplied by a transpose.
00:56
We have to show this will evaluate to identity.
00:59
Now, what is a transpose of transpose? this is going to be a multiplied by a transpose which we already know is equivalent to identity.
01:07
So it is proved this will imply a transpose is orthogonal.
01:17
Similarly, if i talk about the second part of the question, which is we have to show a inverse is orthogonal...
