00:01
If a and b are symmetric matrices and given a b equal to b, then we need to find a inverse b, whether it is symmetric, skew symmetric, okay.
00:12
For that, a is symmetric.
00:16
Okay, implies a transpose equal to a.
00:26
A transpose is equal to a.
00:29
And b symmetric implies b transpose equal to b.
00:36
Okay, so we have this.
00:38
And they have given ab equal to ba.
00:47
Now, we can check whether ab transpose equal to ab, that is, ab is symmetric or not.
01:01
A .b equal to b, then instead of b, we can write b transpose.
01:07
And instead of a, we can write a transpose, that is b transpose, sorry, b transpose into a transpose.
01:20
And with the result, we know that b transpose, a transpose equal to ab whole transpose.
01:27
Then looking at b whole transpose equal to ab, which implies ab is symmetric...