Show that is a solution of the matrix equation X 2 - 2X - 3I = 0 where I is the unit matrix of order 2.

Given, X 2 - 2X - 3I = 0 Putting value of X and I in above equation we get, Since, L.H.S. = = R.H.S. Hence, proved that X 2 - 2X -3I = 0. ∴ is a solution of the matrix equation X 2 - 2X - 3I = 0