The Inverse

Practice Questions

Linear Algebra › The Inverse

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1

Determine the inverse of matrix A where

$A=\begin{bmatrix} 2&-8 \ 1&4 \end{bmatrix}$

2

True or false:

If a matrix with four rows and four columns has an inverse, then the inverse also has four rows and four columns.

3

True or false: A matrix with five rows and four columns has as its inverse a matrix with four rows and five columns.

4

is an involutory matrix.

True or false: It follows that $A^{-1}$ is also an involutory matrix.

5

Determine the inverse of matrix A where

$A=\begin{bmatrix} 32&1 \ 5&8 \ -1&6 \end{bmatrix}$

6

and are both two-by-two matrices. has an inverse.

True or false: Both and have inverses.

7

Suppose that is an invertible matrix. Simplify $AAA^{-1}AAA^{-1}A^{-1}A$ .

8

and are both singular two-by-two matrices.

True or false: must also be singular.

9

Determine the inverse of matrix A where

$A=\begin{bmatrix} 2&-1 \ 5&2 \end{bmatrix}$

10

Find the inverse of the matrix $\begin{bmatrix} 1 & -2\ -3& 3\end{bmatrix}$

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