Question

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

• A. $4x5$
• B. $3x7$
• C. $4x3$
• D. $5x7$

Answer 1

The correct option is D $5x7$

By operation of matrixes (4),

order of$A=4\times 3$

So, By the property of transpose(8),

Order of $A^T=3\times 4.$

The order of $B=4\times 5.$

So, order of $A^{T}B=3\times 5.$

order of $(A^{T}B{)}^T=5\times 3.$

and order of $C^T=3\times 7.$

So, order of $(A^{T}B{)}^T{C}^T=5\times 7.$