00:01
Hi, here we have to find whether the given statements are true or false, where a, b, c are invertible matrices.
00:18
So the first statement is a, b, c inverse of that into a, b, c, b, c, in bracket, a inverse, b, c, inverse of that.
00:43
Now this is equal to c inverse of inverse becomes c into b inverse into a inverse into a, b c, b c, now here we'll get c inverse, b inverse, and a inverse of inverse is a.
01:06
Now this is equal to a a inverse will become i b inverse b will become i so what we get is c c and here c inverse will become i b b inverse will become i so we'll get c c a which is not equal to c b b b inverse will become i so we'll get c c a which is not equal to c b a this implies the statement given there is now the second statement is determinant of b transpose a inverse c b inverse c transpose a transpose a into c inverse.
02:04
Now this is equal to now determinant of b transpose is same as determinant of b.
02:10
Determinant of a inverse is 1 upon determinant of a into determinant of c into 1 upon determinant of b into determinant of c into determinant of a upon determinant of c.
02:43
Now this is equal to now the determinant of b get cancelled with this determinant of b.
02:51
This determinant of c get cancelled with its determinant of c.
02:54
So what remains is determinant of c, which implies the given statement is true...