The Book of Mormon is a book of scripture that complements the Holy Bible. The Bible was written in the old world and the Book of Mormon was written in the new world. They both testify of Jesus Christ and His mission as our Savior and Redeemer. 

A prophet in the Book of Mormon gave this invitation with a promise in Moroni 10:3-5:

"3 Behold, I would exhort you that when ye shall read these things, if it be wisdom in God that ye should read them, that ye would remember how merciful the Lord hath been unto the children of men, from the creation of Adam even down until the time that ye shall receive these things, and ponder it in your hearts.

4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.

5 And by the power of the Holy Ghost ye may know the truth of all things."

You can know for yourself if the book is of God. The promise is that if you read the book and think about it's teachings and ask God if it is true, you will know for yourself if it is.

Christ Himself gave a similar promise in the Bible in John 7:17

"17 If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself."