If A is a 3×3 invertible matrix, show that for any scalar k ≠ 0, (kA)⁻¹ = (1/k)A⁻¹. Hence calculate (3A)⁻¹, where A = [[2,-1,1],[-1,2,-1],[1,-1,2]]

Question

TextInvertible Matrix and Its DefinitionFinding Inverse of Matrix Using Elementary OperationsInverse of a Square Matrix Using Adjoint

If A = [1 –2 0; 2 –1 –1; 0 –2 1], find A⁻¹ and use it to solve the following system of equations : x – 2y = 10, 2x – y – z = 8, – 2y + z = 7

If A = [–1 a 2; 1 2 x; 3 1 1] and A⁻¹ = [1 –1 1; –8 7 –5; b y 3], find the value of (a + x) – (b + y).