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  • 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 A. m × m B. n × n C. n × m D. m × n

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
A. m × m
B. n × n
C. n × m
D. m × n

Answers (1)

As AB’ is defined. So, B’ must have n rows.

∴ B has n columns.

And, B’A is also defined. As, A’ has order n × m

∴ B’A to exist B must have m rows.

∴ m × n is the order of B.
Hence we can say that,

Option (D) is the correct answer.

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infoexpert22

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