NDA 2018 Maths · Mathematics · Matrices · easy

For square matrices A and B of the same order: 1. (AB)^T=B^TA^T. 2. AB=BA.

Single correct option

Consider the following statements for square matrices

A

and

B

of the same order: 1.

(AB)^T=B^TA^T

. 2.

AB=BA

. Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

The reversal law for transposes holds for any compatible matrices, so statement 1 is true. Matrix multiplication is not commutative in general: for

A=\begin{pmatrix}1&1\\0&1\end{pmatrix}

and

B=\begin{pmatrix}1&0\\1&1\end{pmatrix}

AB\ne BA

. Hence only statement 1 is correct.

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