00:01
The matrix a and b have the order order three means a and b are three cross three matrix.
00:19
So its order is three.
00:21
Now we have determinant of a is equals to five and determinant of b equal to nine.
00:31
So this determinant of a can be written as mod of a.
00:34
So mod of a equal to minus five and determinant of b can be written as mod of b and which is equal to nine.
00:43
Now we know that we know that mod of k a is equal to k to the power n into mod of a for any invertible matrix a invertible matrix a and n is the n is the order of the matrix order of the matrix a matrix a.
01:16
So thus determinant of ab determinant of ab is equal to mod of ab is equal to mod of a into mod of b and since the order determinant of a that is mod is minus five and the determinant of b that is mod b is nine.
01:36
So we have five into nine is 45 and minus 45.
01:40
So therefore determinant of ab equal to minus 45.
01:47
Now determinant of minus two a equal to mod of minus two a and which is equal to minus two to the power three into mod of a since the order of order of matrix a matrix a is three.
02:05
So we take two minus two to the power three and which is equal to minus two to the power three is minus eight into mod of a and which is equal to minus eight into the mod a is minus five.
02:17
So we have minus eight into minus five is 40...