Let's find the size of A step by step: B has size 3×4. For AB to be defined, if A is m×n, then n must equal 3 . So A is m×3, and AB‌‌ has size ‌‌(m×3)(3×4)=(m×4). Since AB is an identity matrix, it must be square. Hence m=4. Therefore A is 4×3.