00:01
In this question, we are given the inverses of the matrices a and b, and we are asked to find a -b -inverse and a -transpose inverse.
00:11
To calculate the formula for calculating a -b -inverse is b -inverse times a -inverse.
00:22
So we just need to multiply the matrices, b -inverse and a -inverse.
00:45
To calculate the product, we need to perform the standard matrix by matrix multiplication, and we will solve.
00:53
First row times the first column will give us 6 plus 0 minus 12.
01:03
First row times the second column is going to give us negative 24 plus 5 minus 6.
01:11
And the first row times the last column is going to be 12 plus 15 minus 3.
01:19
Now let's move on to the next row.
01:21
We need to multiply the second row by the first column.
01:25
To get negative 2 plus 0 minus 4.
01:29
The second row times the second column is going to be 8 plus 4 minus 2.
01:37
The second row times the last column equals to negative 4 plus 12 minus 1.
01:47
Now let's write down the last row.
01:50
We need to multiply the last row by the first column.
01:53
We are going to get 1 plus 0 plus 16.
01:59
Last row times the second column is negative 4 plus 3 plus 8 and the last row times the last column is 2 plus 9 plus 4.
02:17
All right.
02:19
Now let's calculate the entries.
02:21
We are going to get negative 6.
02:24
Negative 30 plus 5 is negative 25.
02:30
12 plus 12 is 24.
02:33
The second row is going to be negative 6.
02:37
10 and 7.
02:42
The last row is going to be 17, 7 and 15.
02:53
So this is an inverse of ab...