Specialist Mathematics Β· Unit 1 Β· Matrices Β· Matrix arithmetic and algebra

Use matrix algebra properties, including 𝑨 + 𝑩 = 𝑩 + 𝑨 (commutative law for addition) 𝑨 + 0 = 𝑨 (additive identity) 𝑨 + (βˆ’π‘¨) = 0 (additive inverse) 𝑨𝑰 = 𝑨 = 𝑰𝑨 (multiplicative identity) π‘¨π‘¨βˆ’1 = 𝑰 = π‘¨βˆ’1𝑨 (multiplicative inverse) 𝑨(𝑩 + π‘ͺ) = 𝑨𝑩 + 𝑨π‘ͺ (left distributive law) (𝑩 + π‘ͺ)𝑨 = 𝑩𝑨 + π‘ͺ𝑨 (right distributive law)

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Use matrix algebra to solve matrix equations that involve matrices of up to dimension 2 Γ— 2, including those of the form 𝑨𝑿 = 𝑩, 𝑿𝑨 = 𝑩 and 𝑨𝑿 + 𝑩𝑿 = π‘ͺ, with and without technology.
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