{\displaystyle {\begin{bmatrix}-1&0\\0&1\end{bmatrix}}}[3/2002/3]{\displaystyle {\begin{bmatrix}3/2&0\\0&2/3\end{bmatrix}}}[3/2003/2]{\displaystyle {\begin{bmatrix}3/2&0\\0&3/2\end{bmatrix}}}[cos⁡(π/6R)−sin⁡(π/6R)sin⁡(π/6R)cos⁡(π/6R)]{\displaystyle {\begin{bmatrix}\cos(\pi /6^{R})&-\sin(\pi /6^{R})\\\sin(\pi /6^{R})&\cos(\pi /6^{R})\end{bmatrix}}}Under the 1-to-1 correspondence between matrices and linear maps, matrix multiplication corresponds to composition of maps:[9] if a k-by-m matrix B represents another linear map g : Rm → Rk, then the composition g ∘ f is represented by BA since(g ∘ f)(x) = g(f(x)) = g(Ax) = B(Ax) = (BA)x.The last equality follows from the above-mentioned associativity of matrix multiplication.The rank of a matrix A is the maximum number of linearly independent row vect