This community is invite only. If you're enrolled in Mark's Linear Algebra II class but haven't received an invite, just let him know!

This is a bit of a variation on problem 1.7.2 from our text.

Let $A \in \mathbb R^{n\times n}$. How many multiplications are required to compute $A^8$?

Since A is a square matrix we can use the formula: $$\frac{(n^3)-n}{3}, n = 8$$ Which comes to 168

Edit: is this problem asking how many multiplications are needed to compute an n x n matrix by itself 8 times?

@dan Hmm... $n$ refers to the dimension of the matrix, not the matrix power. It's not 8; rather; it's unspecified so that your final answer should depend upon $n$.

## Comments

Since A is a square matrix we can use the formula:

$$\frac{(n^3)-n}{3}, n = 8$$

Which comes to 168

Edit: is this problem asking how many multiplications are needed to compute an n x n matrix by itself 8 times?

@dan Hmm... $n$ refers to the dimension of the matrix,

notthe matrix power. It's not 8; rather; it's unspecified so that your final answer should depend upon $n$.