यदि (If)` A [(3,-4),(-1,2)]`, एक आव्यूह B निकाले ताकि AB = I.

Explanation

दिया है ,AB = I
`therefore B = A` का inverse = ` A^(-1) `
दिया है , ` A [(3,-4),(-1,2)]therefore "adj A" = [(2,4),(1,3)]`
तथा `।A।= 3 xx 2- (-1) (-4) = 2 ne 0 `
` therefore A^(-1) = (1)/(।A।)"adj A" = (1)/(2) [(2,4),(1,3)]=[(1,2),((1)/(2) ,(3)/(2))]`
Second method :
माना कि `B= [(a,b),(c,d)]` दिया है , AB = I
`rArr [(3,-4),(-1,2)][(a,b),(c,c)]=[(1,0),(0,1)]`
` rArr [(3a-4c,3b -3d),(-a + 2c , -b + 2d)]=[(1,0),(0,1)]`
` therefore 3a - 4c = 1 `।।।(1)
`3b - 4d = 0 ` ...(2)
` - a + 2c = 0 ` ...(3)
` - b + 2d = 1 ` ।।।(4)
(1) तथा (3) को हल करने पर , हमे मिलता है , `a= 1, c = (1)/(2)`
(2) तथा (4) को हल करने पर , हमे मिलता है , `b= 2, d = (3)/(2)`
अतः ` B= [(1,2),((1)/(2) ,(3)/(2))]`