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Questions  >>  CBSE XII  >>  Math  >>  Matrices
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True or False: If $A =\begin{bmatrix} 2 & 3 & 1 \\ 1 &4 & 2 \end{bmatrix}\; and\; B=\begin{bmatrix}2 & 3 \\ 4& 5 \\ 2 & 1 \end{bmatrix},$ then AB and BA are defined and equal.

In this question, AB and BA need not be evaluated. While AB is a 2 X 2 matrix, BA is a 3 X 3 matrix by definition of matrix multiplication. By definition of equality of two matrices, since they are not of the same type, AB is not equal to BA. So the statement is false. This could be taken as an alternate solution.
commented Apr 18, 2013 by jayashri.vasudevan
edited Apr 18, 2013 by jayashri.vasudevan

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