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If the order of A is 4 x 3, the order of B is 4 x 5 and the order of C is 7 x 3 then the order of ${(A^{T} B)}^{T} C^{T}$ is

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4 x 5

3 x 7

4 x 3

5 x 7

answer is D.

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Detailed Solution

$A_{4 \times 3} \Rightarrow A_{3 \times 4}^{T}, B_{4 \times 5} \Rightarrow B_{4 \times 5}^{T}, C_{7 \times 5} \Rightarrow C_{3 \times 7}^{T}$

${(A^{T} B)}^{T}_{5 \times 3}$

${(A^{T} B)}^{T} C^{T} = (5 \times 3) (3 \times 7) = 5 \times 7$

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