If A is a matrix of order (m × n) such that AB and BA are both defined, then B is a/an :
m × n matrix
n × m matrix
m × m matrix
n × n matrix
Matrices
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Question

If A is a matrix of order (m × n) such that AB and BA are both defined, then B is a: 1. m × n matrix 2. n × m matrix 3. m × m matrix 4. n × n matrix

KnowledgeBoat · Accepted Answer

If A is of order m × n:

For matrix multiplication AB to exist, the number of columns of A must equal the number of rows of B.

Number of rows in B = n

For matrix multiplication BA to exist, the number of columns of B must be equal to the number of rows of A.

Number of columns in B = m.

B is of order = n × m.

Hence, option 2 is the correct option.

Mathematics