For some , let and be such that . Then is equal to...

14A-8I $ aligned & B^3=(arraycc 8 & 8 \\ 8 & 16 array)+(arraycc -3 & 0 \\ 0 & -3 array)=(arraycc 5 & 8 \\ 8 & 13 array) \\ & A^3-B^3=(arrayll 20 & 28 \\ 14 & 20 array)-(arraycc 5 & 8 \\ 8 & 13 array)=(arraycc 15 & 20 \\ 6 & 7 array) \\ & |A^3-B^3|=105-120=-15 \\ & |adj(~A^3-B^3)|=|A^3-B^3|=-15 \\ & ...

For some alpha beta in R let A beginarrayll alpha and 2 1 : null (Mathematics)

For some

\alpha, \beta \in R

, let

A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right]

and

B=\left[\begin{array}{ll}1 & 1 \\ 1 & \beta\end{array}\right]

be such that

A^{2}-4 A+2 I=B^{2}-3 B+I=O

. Then

\left(\operatorname{det}\left(\operatorname{adj}\left(\mathrm{A}^{3}-\mathrm{B}^{3}\right)\right)\right)^{2}

is equal to

\_\_\_\_

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For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

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Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

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