Thanks all in the thread for explanations. I had matrix multiplication at the Uni (IT faculty, many years ago) as part of algebra courses, I memorized, I passed the exam, and forgot the topic. Though, I don't remember anyone explaining it then why it's used or useful.

My early understanding after reading your responses and the wiki article, it that's useful if we have some input data (vector), which then undergoes some sequential manipulation by several functions, and we want to know the result in one step, instead of many?