Question

if `A = [(3,x),(0,1)], B = [(9,16),(0,-y)]`, Find x and y  where `A^2 = B`

Answer 1

Given `A = [(3,x),(0,1)], B = [(9,16),(0,-y)]` and `A^2 = B`

Now `A^2 =  A xx A = [(3, x),(0,1) ]xx [(3,x),(0,1)] = [(9, 3x + x),(0,1)] = [(9,4x),(0,1)]`

We have `A^2 = B`

Two matrices are equal if each and every corresponding element is equal.

Thus `[(9,4x),(0,1)] = [(9,16),(0,-y)]`

`=> 4x = 16 and 1 = -y`

`=> x = 4 and y = -1`