6 resources.
Operations on matrices: addition, scalar multiplication and matrix multiplication with worked 3×3 and 2×2 examples, why AB ≠ BA, the transpose of a product, and common mistakes.
Special types of matrices: diagonal, scalar, identity, zero and triangular matrices, how they multiply and their determinants, finding missing entries, worked examples and common mistakes.
Symmetric and skew-symmetric matrices: definitions, splitting any square matrix into both, a 2×2 and a 3×3 worked example, key properties including the zero determinant of odd-order skew matrices, and common mistakes.
What a square matrix is, how to square a matrix, determinant properties including |kA| and |adj A|, idempotent matrices, singular systems, and common mistakes.
Solving a system of linear equations using matrices: the matrix method X = A⁻¹B with the adjoint, worked 2×2 and 3×3 examples, the consistency test, and common mistakes.
Eigenvalues and eigenvectors: the characteristic equation, two fully worked 2x2 examples, the trace and determinant checks, eigenvalues of A², A⁻¹ and A + kI, triangular matrices, and common mistakes.