Question

If order of A, B, C are $3\times 4,5\times 4,5\times 8$ then if the order of $\left(A{B}^{T}C\right)ism\times nthenfindm+n$

Answer 1

Order of $A=3\times 4$

Order of $B=5\times 4$

Order of $C=5\times 8$

To find Order of $A{B}^{T}C$

Order of $B^T=4\times 5$ (Order of $X^T=x+y$, If order of $X=x+y$)

Order of $A{B}^T=3\times 5$

$=A_{3\times 4}{B}_{4\times 5}^T=A{B}_{4\times 5}^T$

Order of $A{B}^{T}C$

$={\left(A{B}^T\right)}_{3\times 5}{C}_{5\times 8}={\left(A{B}^{T}C\right)}_{3\times 8}$

Answer=Order of $A{B}^{T}C=3\times 8$

$m=3,n=8\therefore m+n=11$