In matrix algebra, there are several basic operations that we commonly encounter. Let's explore each of them briefly:

1. Addition: Addition of two matrices is possible only when they have the same dimensions (same number of rows and columns). The sum of two matrices is obtained by adding corresponding elements. For example, if we have two matrices A and B, their sum would be denoted as C = A + B, where every element cij in C is obtained by adding corresponding elements from A and B: cij = aij + bij.

2. Subtraction: Similar to addition, subtraction is only possible when the matrices have the same dimensions. The difference between two matrices A and B is obtained by subtracting corresponding elements. For example, C = A - B, where cij = aij - bij.

3. Scalar Multiplication: Scalar multiplication involves multiplying a matrix by a single scalar value. Each element in the matrix is multiplied by the scalar value. For instance, if we have a matrix A and a scalar c, their product would be denoted as D = cA, where each element dij in D is obtained by multiplying the corresponding element from A with the scalar value: dij = c * aij.

4. Matrix Multiplication: Matrix multiplication is a little more complex compared to the previous operations. When multiplying two matrices A and B, the number of columns in A must be equal to the number of rows in B. The product of matrices A and B is denoted as AB, and each element cij in the resulting matrix C is obtained by multiplying the corresponding row elements from A with the corresponding column elements from B and summing them up: cij = a1j * b1i + a2j * b2i + ... + anj * bni.

These basic operations are crucial in various mathematical applications, such as solving systems of linear equations, finding eigenvalues and eigenvectors, and performing transformations in computer graphics.

Remember to practice these operations to enhance your skills in matrix algebra! You got this!