If the order of matrix 2x3 and B is 3x2, what is the order of AB?

Identify Matrix Dimensions: Step 1: Identify the dimensions of matrices A and B. Matrix A is 2x3, and Matrix B is 3x2. Check Multiplication Possibility: Step 2: Determine if multiplication is possible. 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 2x2.

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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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Q. If the order of matrix

2 \times 3

and

B

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 $2 \times 2$ .