00:01
In this question, we have given a matrix a such that a is a n -cross -n -fair matrix such that a transpose is invertible.
00:16
We need to see that which of the falling given statements are true or false, that is which are correct and which are not.
00:27
The first given condition is a inverse is equal to a transpose.
00:34
Let us consider a square matrix 1, 2, 3 and 4.
00:39
Now as a.
00:42
Now a inverse is given by 4, negative of 3, negative of 2, 1.
00:50
And a transpose is given by 1, 2, 3 and 4.
00:56
Clearly a inverse is not equal to a transpose therefore this is not correct further the second given condition is that a raised to per n inverse is equal to a inverse raise to par n again for the similar matrix a one two three four a raise to per n is given by 1 raise to per n, 2 raise to par n, 3 raise to per n, 4 raise to per n.
01:40
And therefore, a inverse is given by 4 raise to per n, negative of 3 raise to per n, negative of 2 raise to per n, and 1 raise to par n.
01:54
Also, a inverse is given by 1, negative of 3, negative of 2, 4 and 1.
02:04
Therefore, a inverse raised to par n is given by 4 raised to par n, negative of 3 raised to par n, negative of 2 raise to par n, and 1 raise to par n.
02:16
Clearly a raised to par n inverse is equal to a inverse race to par m therefore this condition is correct so the next given option is a transpose inverse is equal to a inverse transpose now a transpose is given by one two three and four and and a transpose inverse would be given by 4, negative of 2, negative of 3, 1...