Matrix Operations in Linear Algebra

Matrix operations are fundamental in linear algebra. They help in solving systems of linear equations, transformations, and many other applications. Below are some of the common matrix operations:

Addition and Subtraction: Similar to the addition and subtraction of numbers, matrix addition and subtraction are performed element-wise.
```
If A and B are matrices of the same size, then A + B and A - B are also matrices of the same size.
```
Multiplication: Matrix multiplication is more complex and requires that the number of columns in the first matrix is equal to the number of rows in the second matrix.
```
If A is an m×n matrix and B is an n×p matrix, then the product AB is an m×p matrix.
```
Transpose: The transpose of a matrix flips it over its diagonal. If A is an m×n matrix, then its transpose A^T is an n×m matrix.
```
(A^T)_{ij} = A_{ji}
```
Inverse: The inverse of a matrix is a matrix that, when multiplied by the original matrix, gives the identity matrix.
```
If A is an n×n matrix and A^(-1) is its inverse, then AA^(-1) = A^(-1)A = I
```

More Resources

For a deeper understanding of matrix operations, you can check out our Introduction to Linear Algebra guide.