Given #A=((-1, 2), (3, 4))# and #B=((-4, 3), (5, -2))#, how do you find #A^-1#?

1 Answer
May 28, 2016

#A^{-1}=((-2/5, 1/5),(3/10, 1/10))#.

Explanation:

There is a rule to calculate the inverse of a #2\times 2# matrix.
If we have a matrix #M# with components
#M=((a, b),(c, d))# the inverse is
#M^{-1}=1/(ad-bc)((d, -b),(-c, a))#.

We can apply this to the matrix #A# and obtain

#A^{-1}=1/(-1*4-2*3)((4,-2),(-3,-1))#
#=1/(-10)((4, -2),(-3, -1))#
#=((-4/10, 2/10),(3/10, 1/10))#
#=((-2/5, 1/5),(3/10, 1/10))#.

Unfortunately I do not understand what should be the role of B because to invert a matrix you don't need another matrix.