Linear Algebra: Verifying A^2-2A+7I=0

[Mathematicsss]

Homework Statement

Verify that A^2-2A+7I=0

Homework Equations

A is a squared matrix and I is the identity matrix.

The Attempt at a Solution

I squared a matrix, which I called A, by multiplying the two A matrices together, then I subtracting the new matrix with the third matrix 2A, then I added 7I , however I did not get the zero matrix, why is that?

 

[Mark44]

Homework Statement

Verify that A^2-2A+7I=0

Homework Equations

A is a squared matrix and I is the identity matrix.

The Attempt at a Solution

I squared a matrix, which I called A, by multiplying the two A matrices together, then I subtracting the new matrix with the third matrix 2A, then I added 7I , however I did not get the zero matrix, why is that?

What was the matrix A that you were working with? I'm pretty sure that A was given as a specific matrix.

 

[Ray Vickson]

Homework Statement

Verify that A^2-2A+7I=0

Homework Equations

A is a squared matrix and I is the identity matrix.

The Attempt at a Solution

I squared a matrix, which I called A, by multiplying the two A matrices together, then I subtracting the new matrix with the third matrix 2A, then I added 7I , however I did not get the zero matrix, why is that?

A "square" matrix is not a "squared" matrix. If $A$ is a square matrix, $A^2$ is a squared matrix. But, terminology aside, the equation you want to verify needs a specific matrix $A$ to begin with; it is false for most $2 \times 2$ matrices, but is true for some of them.

 

[I like Serena]

It's true for $A=\begin{pmatrix} 1 & \sqrt 6 \\ -\sqrt 6 & 1 \end{pmatrix}$ and any matrix that is similar.
It's not true for any other 2x2 matrix.