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If ABT is defined as a square matrix then what is the order of the matrix B, where matrix A has order 2 × 3.

If ABT is defined as a square matrix then what is the order of the matrix B, where matrix A has order 2 × 3. Correct Answer 2 × 3

Concept:

For matrix A(p × r) and B(s × t), AB is defined only if r = s and the order of AB is p × t.

The transpose of a matrix is when columns become rows and rows become columns. 

Calculation:

Let the matrix B has an order p × q, i.e, 'p' rows and 'q' columns

Transpose of B is B' will have to order q × p

For matrix  ABT = is defined, so 

∴ q = 3

Given: ABT is a square matrix

ABT = is square matrix, so

∴ p = 2

So, the order of B = p × q = 2 × 3

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