- From: Malik
*Subject: Matrices*
Tell me about matrices, including addition, subtraction and multiplication. |

First, matrices can only be added if they have the same number of rows and columns.

If this is the case, we say that the matrices are **conformable** for addition.

If the matrices are conformable, simply add the corresponding elements:

Matrices are **conformable** for subtraction if they have the same number of rows and columns.

Subtract the elements of the second matrix from the corresponding elements of the first:

Matrices are **conformable** for multiplication if the number columns in the first matrix is equal to the number of rows in the second.

**NB**: The order of the matrices is important for matrix multiplication.

In general, **A** × **B** is not equal to **B** × **A**.

In general a *p* × *q* matrix multiplied by a *q* × *r* matrix results in a matrix that is *p* × *r* in shape.

Split the left matrix into rows, and the right matrix into columns.

To find the **top-left** element of the answer matrix,

Take the **top** row of the first matrix,

and the **left** column of the second matrix.

Multiply corresponding elements, and add.

Repeat with each row/column combination to fill the entire matrix, as shown below.

*Click* Refresh *to see the step-by-step working again*

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