1. ## Matrices

Find $A^2$

a) A= $\begin{bmatrix} 1 & 3 & 5 \\ 2 & 4 & -3 \end{bmatrix}$

b)A= $\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$

c) A= $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$

I don't understand how to calculate the power of a matrix.

Can you show me step by step on how to do one of them? Thanks

2. Originally Posted by Linnus
Find $A^2$

a) A= $\begin{bmatrix} 1 & 3 & 5 \\ 2 & 4 & -3 \end{bmatrix}$

b)A= $\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$

c) A= $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$

I don't understand how to calculate the power of a matrix.

Can you show me step by step on how to do one of them? Thanks
$A^2 = A \, A$. I assume you know how to multiply matrices. If you do, you should notice that $A^2$ is not defined for any of them. $A^2$ is only defined if A is a square matrix.

3. I know that $A^2=AA$

I also know that the matrices doesn't "fit" that is why I'm lost on how to solve these matrices.

Does that mean there is no answer for them?

4. Originally Posted by Linnus
I know that $A^2=AA$

Does that mean there is no answer for them?
correct.

to multiply two matrices, the number of columns in the first must be equal to the number of rows in the second. if it is the same matrix, this implies the matrix must be square. that is not the case with any of the matrices in your problem