4. Matrix Algebra

Matrix Multiplication — Quiz

Test your understanding of matrix multiplication with 5 practice questions.

Practice Questions

Question 1

If $A$ is a $2 \times 3$ matrix and $B$ is a $3 \times 4$ matrix, what are the dimensions of $AB$?

Question 2

Compute $AB$ where $A=\begin{bmatrix}2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}4\\5\end{bmatrix}$.

Question 3

Compute $AB$ where $A=\begin{bmatrix}1 & 2\\0 & -1\end{bmatrix}$ and $B=\begin{bmatrix}3 & 4\\5 & 6\end{bmatrix}$.

Question 4

Which condition must hold for the product $AB$ to be defined?

Question 5

Let $A$ be any $2 \times 3$ matrix and let $I$ be the $3 \times 3$ identity matrix. What is $AI$?