Advertisements
Advertisements
Question
If `A = [[-3,1],[-4,3]]` and A-1 = αA, then α = ______.
Options
5
-5
`1/5`
`-1/5`
MCQ
Fill in the Blanks
Solution
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`
shaalaa.com
Is there an error in this question or solution?
