KCET 2025 Math Paper

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.