आव्यूह `[{:(2,3),(5,7):}]` का व्युत्क्रम आव्यूह होगा -

Options

A. `A^(-1)=[{:(-7," "3),(5,-2):}]`
B. `A^(-1)=[{:(-4," "3),(5,-3):}]`
C. `A^(-1)=[{:(-7," "2),(9,-2):}]`
D. `A^(-1)=[{:(-7," "1),(2,-2):}]`

Answer

A

Explanation

मान `A=[{:(2,3),(5,7):}]`
हम जानते हैं कि `A A^(-1)=I`
`[{:(2,3),(5,7):}]A^(-1)=[{:(1,0),(0,1):}]`
`rArr[{:(1,(3)/(2)),(5,7):}]A^(-1)=[{:((1)/(2),0),(0,1):}] " " R_(1)to(1)/(2)R_(1)`
`rArr[{:(1,(3)/(2)),(0,(-1)/(2)):}]A^(_1)=[{:((1)/(2),0),((-5)/(2),1):}] " " R_(2)toR_(2)-5R_(1)`
`rArr[{:(1,(3)/(2)),(0,1):}]A^(_1)=[{:((1)/(2),0),(5,-2):}] " " R_(2)to-2R_(2)`
`rArr[{:(1,0),(0,1):}]A^(-1)=[{:(-7," "3),(5,-2):}] " " R_(1)toR_(1)-(3)/(2)R_(2)`
`rArrA^(-1)=[{:(-7," "3),(5,-2):}]`.