矩阵的逆

Introduction

Invertible Matrices

Computing the Inverse Matrix

Solving Linear Systems using Inverses

Invertible linear transformations

Which matrix is the inverse of

Let $A$ and $B$ be invertible $n\times n$ matrices. Which matrix is $(AB)^{-1}$?

Row reduce the augmented matrix $\left(\begin{array}{c|c} A & I_n \end{array}\right)$ until the left half is the identity matrix. The inverse $A^{-1}$ is then the ______ half of the result. Enter one word.

Enter the entry in the first row and second column of

(a number).

Let

Use Gauss-Jordan elimination on $\left(\begin{array}{c|c} U & I_3 \end{array}\right)$ to find $U^{-1}$, then enter the entry in the first row and third column of $U^{-1}$ (a number).

Let $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$. The matrix $A$ is invertible exactly when which quantity is nonzero?

Find the inverse of

and enter the four entries of $A^{-1}$ in order $a,b,c,d$ reading rows left to right, top to bottom.