To show that (AB)-1 = B-1 A-1, we can start by finding the inverse of AB.
The inverse of a product of matrices AB is given by:
(AB)-1 = B-1 A-1
where A and B are invertible matrices.
To find A-1, we need to solve the equation A x A-1 = I, where I is the identity matrix.
From the given information, we know that A = L'. The inverse of L' is L, so we have:
A-1 = L
To find B-1, we need to solve the equation B x B-1 = I. Since B is a scalar matrix with a value of 12, we have:
B-1 = 1/12
Now we can substitute the values of A-1 and B-1 into the formula for (AB)-1:
(AB)-1 = B-1 A-1
Substituting the values of A-1 and B-1, we get:
(AB)-1 = (1/12) L
Therefore, we have shown that (AB)-1 = B-1 A-1 is true.