Compute A^2-2A+I.

Question

Answer 1

You can save a little calculation time by noting:

A² – 2A + 1 = (A – I)² .

So A – I = |1 0|

|9 3|

So this matrix just has to be multiplied by itself. Remember each row in first matrix gets multiplied times each column in second matrix. To be more specific, to find i,j entry in the produce multiply row

|1 0| |1 0|

|9 3| X |9 3|

So the 1,1 entry is 1*1 + 0*9 = 1, 1st row times 1st col.

The 1,2 entry is 1*0 + 0*3 = 0, 1st row times 2nd col.

The 2,1 entry is 9*1 + 3*9 = 36, 2nd row times 1st col.

The 2,2 entry is 9*0 + 3*3 = 9, 2nd row times 2nd col.

And the answer is |1 0|

|36 9|

Robert Clark