Question

assume that A and B are invertible matrices of the same order. 25. Simplify (AB⁻¹)⁻¹. 26. Simplify (A⁻¹B)⁻¹.

Answer 1

To simplify (AB⁻¹)⁻¹, we can apply the rule that the inverse of the product of matrices is equal to the product of their inverses in reverse order. To simplify (A⁻¹B)⁻¹, we apply the same rule.

Step-by-step explanation:

To simplify (AB⁻¹)⁻¹, we can apply the rule that the inverse of the product of matrices is equal to the product of their inverses in reverse order. So, (AB⁻¹)⁻¹ = (B⁻¹A⁻¹). This is because when we take the inverse of a product of matrices, we need to reverse the order of the matrices and take the inverse of each matrix individually.

To simplify (A⁻¹B)⁻¹, we can apply the same rule. So, (A⁻¹B)⁻¹ = (BA⁻¹)⁻¹. Again, we reverse the order of the matrices and take the inverse of each matrix individually.