Right off the bat I can say that is loaded question. To put it simply: yes. However, I sense that this answer is always manipulated to justify political opinions. To have a complete answer, we have to unpack that statement and understand that answer into various different contexts. The first one is what was slavery within Africa and the Middle East, second its context in South America and the third is within North America with a focus on the United States.
I am grossly oversimplifying these matters, and you will have to keep in mind that each individual answer to these three contexts merits one or two books by themselves. I assume that based on your question, you are referring to something called chattel slavery which is a specific servitude relationship in which the enslaved person is considered property of the owner. It is typically what Westerners associate with the word “slavery” and it truly is horrifying because it is the complete reduction of an individual to an object and the removal of their agency.
Keep in mind though, the chattel slavery is a very narrow aspect of slavery and does not apply to a lot of servitude relationships in Africa and in the Middle East. Many enslavement relationships in Africa could be called domestic slavery, where enslaved persons would work primarily household of the master but retain some freedoms, could not be sold to others without extreme cause, retained profits from their labor and could marry freely. Which is very different than what happened for instance in the cotton plantations in the Antebellum South. Likewise, pawnship or slavery as a result of debt is also common in Africa and the Middle East. It was a form of collateral in case of debt but it was based on a very defined contract, with clear terms of service, rights, protection and kinship ties. Likewise, there was an extensive slave trade between Africans and Europeans, and many times that argument is used to justify racist beliefs and white supremacy. However, it has to be elaborated that Africa is a not a unified entity but an entire continent with different ethnicities and nations. Capturing your enemies and selling them into European slavery is the same as different European countries raiding each other for resources. In addition, there was a vibrant slave trade in Africa and in the Middle East but as mentioned above; their definitions of slavery were very different than chattel slavery, which was very widespread in Europe and North America.
In South America, the model of chattel slavery was extremely brutal, out of all enslaved Africans, 2/5 went to South America and 2/5 went to the Caribbean with only 1/5 being directed towards North America. The extreme brutality is due to the extreme profitability of the crops being grown there in the 17th-18th centuries: sugarcane. It was labor intensive, back breaking and living conditions were appalling. Disease was rampant and mortality was very high. Since turnover was so high, African communities in South America and in the Caribbean retained a lot of their character from their home areas and likewise, held on to some of the servitude relationships from their home area.
In North America, chattel slavery was dominant and widespread. A series of laws throughout the 13 colonies in the 18th century consolidated the status of enslaved African Americans as property, with no rights or protections. For instance, it was completely legal to kill one’s enslaved person without any legal repercussions. With the abolition of the slave trade in England, there was a reduction of the influx of African slaves to the United States, and thus African American community began to develop. Many times, Emancipation laws were tricky and outright illegal in some areas, which made freeing oneself a challenge. Likewise, even if granted freedom that often did not extend to their immediate family or relatives. Thus, many freed African Americans sought to “buy” their families as a way to protect them from slavery, holding them in nominal possession as a way to ensure their family integrity. Because it was a possibility that even though they were freed, roaming bands of white slave patrols might capture them and sell them into bondage anyway for a profit.
So in the narrative of slavery in the US, it is seen that African Americans did own other African Americans, but we cannot forget that many times it was done as a necessity to combat the separation of families, and as a form of protection in a very unjust and cruel system.
Sources
Berlin, I. (2007). Slaves without masters: The free negro in the antebellum South. New York: The New Press.
Ely, Melvin (2005). Israel on the Appomattox: A Southern Experiment in Black Freedom from the 1790s Through the Civil War. Vintage Press.
Austin, Gareth (2017). "Slavery in Africa, 1804-1936". In David Eltis; Stanley L. Engerman; Seymour Drescher; David Richardson. The Cambridge World History of Slavery: Volume 4, AD 1804–AD 2016. New York: Cambridge University Press.
Schoenbrun, David (2007). "Violence, Marginality, Scorn & Honor: Language Evidence of Slavery in the Eighteenth Century". Slavery in the Great Lakes Region of East Africa. Oxford, England: James Currey Ltd
Paul E. Lovejoy and David Richardson (2001). "The Business of Slaving: Pawnship in Western Africa, c. 1600–1810
http://www.thomaslegion.net/historyofslaveryintheunitedstatesofamerica.html