Question

Example Suppose $A^{-1} = \begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 3 & 1 \\ 2 & -5 \end{bmatrix}$ 1. Find $(A^T)^{-1}$ 2. Find $(AB)^{-1}$

          Example
Suppose $A^{-1} = \begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 3 & 1 \\ 2 & -5 \end{bmatrix}$
1. Find $(A^T)^{-1}$
2. Find $(AB)^{-1}$

Example
Suppose A^-1 =
< b m a t r i x > and B^-1 =
< b m a t r i x >
1. Find (A^T)^-1
2. Find (AB)^-1

Added by Shelly R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Matthew Elliott

Step 1

The inverse of a matrix A is denoted as A^-1 and is defined as the matrix that, when multiplied with A, gives the identity matrix I. Given A = | 3 5 | To find A^-1, we can use the formula: A^-1 = (1/det(A)) * adj(A) where det(A) is the determinant of A and Show more…

Show all steps