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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?
Solution
∵ 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]
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