Question

Find a matrix B of order 2 such that AB = BA = I is the identity matrix of order 2​

Answer 1

Answer:

Let A=⎛⎝⎜111124135⎞⎠⎟ and D=⎛⎝⎜200030005⎞⎠⎟.

It is found that right-multiplication by D multiplies each column of A by the corresponding diagonal entry of D, whereas left-multiplication by D multiplies each row of A by the corresponding diagonal entry of D.

Construct a 3 x 3 matrix B, not the identity matrix or zero matrix, such that AB=BA.