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Question
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is ______.
Options
m × m
n × n
n × m
m × n
Solution
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is m × n.
Explanation:
Order of matrix A = m × n
Let order of matrix B be K × P
Order of matrix B' = P × K
If AB' is defined then the order of AB' is m × K if n = P
If B'A is defined then order of B'A is P × n when K = m
Now, order of B' = P × K
∴ Order of B = K × P
= m × n .....[∵ K = m, P = n]
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