Answer:
1. The matrix A isn't the inverse of matrix B.
2. |B|=12, |A|=12
Step-by-step explanation:
1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.
We have:
and
A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.
Then if A is the inverse of B:
Where,
Observation:
If you have two matrices:
Now:
Then, the matrix A isn't the inverse of matrix B.
2. If you have a matrix A:
The determinant of the matrix is:
Then the determinant of B is:
The determinant of A is: