If A is 3 × 4 matrix and B is a matrix such that ATB and BAT are both defined, then B is of order

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If A is 3 × 4 matrix and B is a matrix such that A^TB and BA^T are both defined, then B is of order

4 × 4

4 × 3

3 × 3

3 × 4

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Since, A is of order 3 × 4.

Thus, order of A^T = 4 × 3

Now, let B has order = m × n

For A^TB to be defined, we must have 3 = m and for BA^T to be defined, n = 4

So, order of B = m × n = 3 × 4