00:01
In this question, we need to find out what is the inverse of the given general rotation matrix.
00:08
Okay, so a is given to be equals to cosine of theta minus sine of theta.
00:15
And here i'm having sine of theta and cosine of theta.
00:19
Correct.
00:21
So first of all, let us try to find it out.
00:25
So first i will try to find what is the determinant of a.
00:28
So this is cosine square theta plus sine.
00:31
Square theta which is equals to one only correct so we know that let me write one note if b is a matrix a b c d then we know that b inverse is given by one divided by determinant of b and here we just change d and a and here the sign gets changed okay so with this i can find out the inverse so a inverse comes out to be one divided by one and then we have to change these two so this becomes cosine theta and cosine theta and here i will get minus sine theta and this will become sine of theta so hence a inverse comes out to be equal to what a inverse will be equals to here you see in this will be cosine of theta correct and this will be sine of theta here what we will get this is minus sine theta.
01:37
So we know that since sine of theta is equals to, sorry, sign of minus theta, it is equals to minus times of sine theta and cosine of theta is same as cosine of minus theta.
01:57
Okay, so we can use this two properties here...