$2.(40$ pts$.)$ In class, we learned how to take small solutions from our toolbox, and combine them to solve larger problems. Assume you have the following building blocks in your toolbox, and no other operation or function not listed:

$+,-,$x$,$ for scalars

$$ if$-$else

$$vector dot product

$$vector addition and sub$-$ length, size, and zeros

commands for matrices

traction, $2+2=$k

$$ loops

$$ matrix addition, A$+$B $=$ C

Using these tools,

$($a$)$ Describe an algorithm to perform the integer multiple of a matrix.

That is$,$ given A compute something like $4$A$.$ Is this a tool that can be added to your toolbox?

$($b$)$ Describe an algorithm to raise, a matrix,

A to an integer power,

i$.$e$.$ compute something like $4$

$.$ Would this be a candidate for

your toolbox?