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

Answer 1

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]