Jesus indicated that they were! And, they are also validated as reliable through the New Testament writings of the early Church leaders.
It is important to realize that prior to Christ’s birth, death, and resurrection, the ONLY Scriptures were those in the Old Testament (currently referred to as the Tenach by the Jews). New Testament books were not written, so when Jesus spoke of the Scriptures, or said, “It is written,” He could not have been speaking of the Gospels, Acts, or the other New Testament books.
Our Savior validated God’s Word when He answered Satan’s challenges by quoting from Deuteronomy 8:3.
Matthew 4:4 But he answered and said, It is written, Man shall not live by bread alone but by every word that proceedeth out of the mouth of God.
Notice, that Jesus also said that those very Scriptures testified about Him.
John 5:39 Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me.
When Jesus was dealing with the leaders of that time, He frequently referred them to the Scriptures, sometimes saying, “It is written,” or, not knowing the scriptures.
Matthew 22:29 Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God.
Jesus often quoted from the Scriptures as in these examples.
Matthew 4:7, 10; 11:10; 21:13; 26:31
In the book of Acts, we find early believers searched those Scriptures daily. They trusted them to help them prove the truth about our Savior and the wonderful things God was accomplishing.
Acts 17:11 These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
And, later, New Testament writings underscored the trustworthiness of the Old Testament. For example, Paul reminded the young evangelist, Timothy, how he had been schooled by them. Paul asserted that those Scriptures were connected to salvation through faith in Christ Jesus.
2 Timothy 3:15 And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus.
Clearly, God wants us to know that we can trust the Old Testament!