- 06-Jul-2022

**Multiplication of 2x3 and 3x3 matrices is possible** and the result matrix is a 2x3 matrix.

Any number multiplied by one results in the same original number. The same goes for a matrix multiplied by an identity matrix, the result is always **the same original non-identity (non-unit) matrix**, and thus, as explained before, the identity matrix gets the nickname of "unit matrix".

A 3×3 matrix has three rows and three columns. In matrix multiplication, **each of the three rows of first matrix is multiplied by the columns of second matrix and then we add all the pairs**.

For matrix multiplication, **the number of columns in the first matrix must be equal to the number of rows in the second matrix**. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.

**Multiplication of 3x3 and 3x1 matrices is possible** and the result matrix is a 3x1 matrix. This calculator can instantly multiply two matrices and show a step-by-step solution.

**You can multiply a 2x3 matrix times a 3x1 matrix but you can not multiply a 3x1 matrix times a 2x3 matrix**. The dimension of the matrix resulting from a matrix multiplication is the first dimension of the first matrix by the last dimenson of the second matrix.

**When we do multiplication:**

- The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.
- And the result will have the same number of rows as the 1st matrix, and the same number of columns as the 2nd matrix.

**In other words, to take the determinant of a 2×2 matrix, you follow these steps:**

- Multiply the values along the top-left to bottom-right diagonal.
- Multiply the values along the bottom-left to top-right diagonal.
- Subtract the second product from the first.
- Simplify to get the value of the 2-by-2 determinant.

**Multiplication of 2x2 and 2x2 matrices is possible** and the result matrix is a 2x2 matrix.

**How to Multiply a Matrix by a Number**

- When you multiply a matrix by a number, you multiply every element in the matrix by the same number.
- For example, if x is 5, and the matrix A is:
- Then, xA = 5A and.
- In the example above, every element of A is multiplied by 5 to produce the scalar multiple, B.

In order for matrix multiplication to be defined, **the number of columns in the first matrix must be equal to the number of rows in the second matrix**.

Definition: Square of a Matrix

In other words, just like for the exponentiation of numbers (i.e., 𝑎 = 𝑎 × 𝑎 ), **the square is obtained by multiplying the matrix by itself**. As one might notice, the most basic requirement for matrix exponentiation to be defined is that 𝐴 must be square.

**Multiplication of 2x3 and 3x3 matrices is possible** and the result matrix is a 2x3 matrix.

So the answer to your question is, a matrix cannot be multiplied by **a matrix with a different number of rows then the first has columns**.

**Multiplication of 2x3 and 3x2 matrices is possible** and the result matrix is a 2x2 matrix. This calculator can instantly multiply two matrices and show a step-by-step solution.

The numbers in a matrix can represent data, and they can also represent mathematical equations. In many time-sensitive engineering applications, **multiplying matrices can give quick but good approximations of much more complicated calculations**.

**Multiplication of 2x2 and 2x1 matrices is possible** and the result matrix is a 2x1 matrix.

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