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Maths-

General

Easy

Question

If A and B are matrices of order m × n and n × m respectively, then the order of matrix B^T (A^T)^T is -

m × n
m × m
n × n
Not defined

The correct answer is: Not defined

To find the order of $B to the power of T open parentheses A to the power of T close parentheses to the power of T$ .
Given, A and B are matrices of order m × n and n × m respectively.
therefore, order of $A to the power of T$ =n x m
order of $open parentheses A to the power of T close parentheses to the power of T$ = m x n.
Order of $B to the power of T$ = m x n.
By the rule of matrix multiplication, number of columns in first matrix must be equal to number of rows in second matrix but in the above case, n is not equal to m.

Therefore, matrix multiplication can not be happened. So order is not defined.

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