Let A be an invertible n × n matrix, and let B be an n × p matrix. Explain why A⁻¹B can be computed by row reduction:
If [ A B] ~ ... ~ [I X], then X = A⁻¹B.
If is larger than 2 × 2, then row reduction of [A B] is much faster than computing both A⁻¹ and A⁻¹B.
