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If the order of matrix $2 \times 3$ and $B$ is $3 \times 2$ what is the order of $AB$

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Determine the direction of a vector scalar multiple

Full solution

Q. If the order of matrix

2 \times 3

and

B

is

3 \times 2

what is the order of

AB

Identify Matrix Dimensions: Step $1$ : Identify the dimensions of matrices $A$ and $B$ . $\newline$ Matrix $A$ is $2 \times 3$ , and Matrix $B$ is $3 \times 2$ .
Check Multiplication Possibility: Step $2$ : Determine if multiplication is possible. $\newline$ For matrix multiplication, the number of columns in the first matrix $A$ must equal the number of rows in the second matrix $B$ . Here, $A$ has $3$ columns and $B$ has $3$ rows, so multiplication is possible.
Calculate Product Matrix Order: Step $3$ : Calculate the order of the product matrix $AB$ . The resulting matrix $AB$ will have the same number of rows as matrix $A$ and the same number of columns as matrix $B$ . So, the order of $AB$ is $2 \times 2$ .

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