If A2×3, B4×3, C2×4 are three matrices, then which of the following is/are defined ?

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If A_2×3, B_4×3, C_2×4 are three matrices, then which of the following is/are defined ?

A

AC^TB

B

B^TC^TA

C

AB^TC

D

All of these

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Given A is a 2 × 3 matrix, B is 4 × 3 matrix and C is 2 × 4 matrix.

Thus, C^T is 4 × 2 matrix.

Therefore, C^TB is not possible.

Now, C^T of order 4 × 2 and A is of order 2 × 3

Therefore, C^TA is a matrix of order 4 × 3.

Also, B^T is of order 3 × 4 and C^TA is of order 4 × 3

∴ B^T(C^TA) is a matrix of order 3 × 3

Hence, option B is correct.

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