Why am I learning about matrices? What are they?!
Square matrices can be thought of simply as transformation operators—rotation, translation, or shear (distortion). A 2x2 matrix transforms a set of 2D coordinates, a 3x3 matrix translates a set of 3D coordinates etc. (Yes! 4D is a thing and its fascinating! See https://www.youtube.com/watch?v=BVo2igbFSPE for a brief visualisation or https://www.youtube.com/watch?v=vQ60rFwh2ig for some interesting trickery. Don't worry! 3D is all you need for A level... and life!) When thinking about matrices as transformation operators, the determinant of the matrix is related to the scaling factor of the transformation. eg. reflection matrices in any dimension have a determinant of -1.
You can also use matrices of any dimensions to solve series of simultaneous equations. Naturally solving two simultaneous equations is easy enough to do by hand, but what about three? Four? Ten? As soon as you hit more than three simultaneous equations, matrices are what you'll need to find the solutions. But again, fear not! At A-level you won't encounter anything more challenging than a 3x3 matrix. Any more than that would just be a mean and boring extension of the same old method.
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