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What a matrix is and the kinds of matrix you meet: square, zero, identity, diagonal and triangular. Then adding matrices, multiplying them and why the order of a product matters, and the transpose with symmetric and skew-symmetric matrices.
The determinant of a 2 by 2 and a 3 by 3 matrix, minors and cofactors, and expansion along any row or column. Then the properties that make a large determinant easy, and the area of a triangle and the test for three points on a line.
The adjoint and the inverse of a matrix, and the test for a matrix that has no inverse. Then solving systems of two and three equations with the inverse, deciding when there is one solution, none or infinitely many, and finding the inverse by row operations. Cramer's rule and models from real life are included.