Question

If `A = [[-3,1],[-4,3]]` and A^-1 = αA, then α = ______.

पर्याय

• 5

• -5

• `1/5`

• `-1/5`

Answer 1

If `A = [[-3,1],[-4,3]]` and A^-1 = αA, then α = `underline(1/5)`.

Explanation:

If `A = [[a,b],[c,d]]` and ad - bc ≠ 0, then

`A^-1=1/(ad-bc)[[d,-b],[-c,a]]`

`A=[[-3,1],[-4,3]]`

`therefore A^-1=1/-5[[3,-1],[4,-3]]=1/5A`

`therefore alpha = 1/5`