Math Problem Statement

se the inverse matrices to find (AB)−1, (AT)−1, and (2A)−1. A−1 =

1 −2

−2 5 ,

B−1 =

1 2

−2 −3

Solution

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Math Problem Analysis

Mathematical Concepts

Matrix Inverses
Matrix Transpose
Scalar Multiplication of Matrices

Formulas

(AB)^{-1} = B^{-1}A^{-1}
(A^T)^{-1} = (A^{-1})^T
(2A)^{-1} = \frac{1}{2}A^{-1}

Theorems

Inverse of a Product Theorem
Transpose of an Inverse Matrix Theorem
Inverse of a Scalar Multiple Theorem

Suitable Grade Level

College-Level Linear Algebra