If A=| 4 1| | 7 2| what will be the matrix B such that AB=I where I is the unit matrix of order 2?

1 Answer
Jan 30, 2018

THe matrix #B=((2,-1),(-7,4))#

Explanation:

The inverse of matrix #A=((a,b),(c,d))# is

#A^-1=1/(ad-bc)((d,-b),(-c,a))#

Here,

#A=((4,1),(7,2))#

If, #AB=I#

Then,

#B=A^(_1)=1/((4*2)-(1*7))*((2,-1),(-7,4))#

#=1/1((2,-1),(-7,4))#

#"Verification"#

#A*B=((4,1),(7,2))*((2,-1),(-7,4))=((1,0),(0,1))=I#