Learn the basic parts of a matrix: rows, columns, and entries
Write a matrix in rectangular form
Add or subtract matrices with the same dimensions by combining matching entries
Multiply a matrix by a scalar by multiplying every entry
Multiply matrices when the inner dimensions match
Use row-by-column multiplication for matrix products
Find the identity matrix for square matrices
Find the transpose by swapping rows and columns
Compute the determinant for square matrices
Find the inverse of a matrix when it exists
Solve systems of equations using matrices
Use row operations to simplify matrices
Reduce matrices to row echelon form or reduced row echelon form
Check dimensions before performing any matrix operation
Verify results by substituting or multiplying back when needed