Matrix Multiplications

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

Calculate the product:

$$\begin{bmatrix} 1 & 2 \end{bmatrix} \times \begin{bmatrix} 3 \\ 4 \end{bmatrix}$$

Which of the following is generally true regarding matrix multiplication?

Multiply the Identity matrix $I$ by any compatible matrix $A$. What is the result?

Given:

$$A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, B = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$

Calculate $AB$.

For matrix multiplication $AB$ to be valid, the number of _____ in A must equal the number of _____ in B.

What is the element at row 1, column 1 of the product of these matrices?

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix}$$