Final answer:
To show that both matrices a and b are invertible, we need to demonstrate that they have inverses.
Step-by-step explanation:
To show that both matrices a and b are invertible, we need to demonstrate that they have inverses. Since ab is invertible, it means that the product of a and b is a non-singular matrix (a matrix with a non-zero determinant).
To show that a is invertible, we can assume that b is not invertible. If b is not invertible, then the determinant of b is zero. But since ab is invertible, the determinant of ab is non-zero.
Using the property that the determinant of a product of matrices is equal to the product of their determinants, we have det(ab) = det(a)det(b). Since det(ab) is non-zero, it implies that both det(a) and det(b) are non-zero. Therefore, both a and b are invertible.