List eight types of matrices and indicate using an example.

1. Square matrix: A matrix with the same number of rows and columns.
Example:
\[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]

2. Diagonal matrix: A square matrix where all elements outside the main diagonal are zero.
Example:
\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix} \]

3. Identity matrix: A diagonal matrix where all elements on the main diagonal are 1.
Example:
\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]

4. Zero matrix: A matrix where all elements are zero.
Example:
\[ \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix} \]

5. Row matrix: A matrix with only one row.
Example:
\[ \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \]

6. Column matrix: A matrix with only one column.
Example:
\[ \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \]

7. Symmetric matrix: A square matrix that is equal to its transpose.
Example:
\[ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{bmatrix} \]

8. Skew-symmetric matrix: A square matrix where the transpose is equal to the negative of the original matrix.
Example:
\[ \begin{bmatrix} 0 & -2 & 3 \\ 2 & 0 & -5 \\ -3 & 5 & 0 \end{bmatrix} \]

1. Null/Zero Matrix: All elements are zero.
- Example: [0 0]
[0 0]

2. Identity Matrix: Main diagonal elements are 1, all other elements are zero.
- Example: [1 0]
[0 1]

3. Diagonal Matrix: Non-zero elements only appear on the main diagonal.
- Example: [2 0 0]
[0 3 0]
[0 0 4]

4. Triangular Matrix: All elements below or above the main diagonal are zero.
- Example: Upper Triangular: [1 2 3]
[0 4 5]
[0 0 6]
Lower Triangular: [1 0 0]
[2 3 0]
[4 5 6]

5. Symmetric Matrix: Transpose is equal to the matrix itself.
- Example: [1 2]
[2 3]

6. Antisymmetric Matrix: Transpose is equal to the negative of the matrix itself.
- Example: [0 1]
[-1 0]

7. Orthogonal Matrix: Inverse is equal to its transpose.
- Example: [1/√2 -1/√2]
[1/√2 1/√2]

8. Invertible Matrix: Has an inverse matrix.
- Example: [2 1]
[1 2]
- Inverse: [1/3 -1/3]
[-1/3 2/3]