Question

If A = `[(2, 0),(0, 1)]` and B = `[(1),(2)]`, then find the matrix X such that A⁻¹X = B.

Answer 1

A^–1X = B

∴ A(A^–1X) = AB

∴ (AA^–1)X = AB

∴ IX = AB

∴ X = `[(2, 0),(0, 1)][(1),(2)] = [(2 + 0),(0 + 2)]`

∴ X = `[(2),(2)]`.