Hello everyone. I'm trying to show ab = ba. //communative property of dot product
This is what I have, is it enough to show this?
ab = (ax, ay, az) (bx, by, bz) = axbx + ayby + azbz;
ab = (axi + ayj) (bxi + byj); //note: i and j are unit vectors
= axbx(i)(i) + ayby(j)(j) + axby(i)(j) + aybx(j)(i)
= axbx+ayby

ba = (bx, by, bz) (ax,ay,az) = bxax + byay + bzaz;

ba = (bxi + byj) (axi + ayj)
= bxax(i)(i) + byay(j)(j) + bxay(i)(j) + byax(j)(i)
= bxax + byay

Is this enough to show the dot product is communative?
Any help would be great if it isn't!