Question

If A and B are any two 2 × 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Answer 1

∵ AB = BA = B

But it is possible, when A = 0 or B = 0

But B is not a zero matrix  ...(Given)

∴ A is a zero matrix

Or A is an identity matrix  ...[∵ IB = BI = BI]