While this is an admittedly overly simplification, it can generally be said that Biblical Hebrew omits the present tense of the verb “to be” in identity statements. In linguistics, this construction is called a zero copula. Exodus 3:6 is an example of such a construction; the verb “am” is in parentheses because it is not present in the Hebrew:

אָנֹכִי אֱלֹהֵי אָבִיךָ 
I (am) the God of thy father

In Ex 3:6, God is not describing Himself as the God of Abraham, Isaac and Jacob, as though there are other gods for other people. Rather, He is identifying Himself as “the God of Abraham, the God of Isaac, and the God of Jacob” (cf. Ex 3:15).

Commentary of Keil & Delitzsch on Exodus 3:6

Jehovah then made Himself known to Moses as the God of his fathers, Abraham, Isaac, and Jacob, reminding him through that name of the promises made to the patriarchs, which He was about to fulfill to their seed, the children of Israel.

Given the above discussion, Jesus’ argument in Mt 22:32b is astonishing in its simplicity. His point is that God would not refer to Himself in such terms, as “the God of Abraham, the God of Isaac, and the God of Jacob,” if those individuals were not still living. While not conclusive on its own, the present tense of εἰμί (Strong’s G1510 meaning I exist, I am) in Mt 22:32 supports this interpretation.

While this is an admittedly over simplification, it can generally be said that Biblical Hebrew omits the present tense of the verb “to be” in subject complement constructions. In linguistics, this phenomenon where the verb is omitted is called a zero copula. Exodus 3:6 is an example of such a construction; the verb “am” is in parentheses because it is not present in the Hebrew:

אָנֹכִי אֱלֹהֵי אָבִיךָ 
I (am) the God of thy father

Subject complements can be predicate adjectives, predicate nouns, or predicate pronouns. The subject complement in Ex 33:6 is a predicate noun (God). In order to determine the function in context, I looked at whether the referent of “God” is unique or non-unique, concluding that it is unique. If so, then the predicate identifies rather than describes the subject. Thus, God is not describing Himself as the God of Abraham, Isaac and Jacob, as though there are other gods for other people. Rather, He is identifying Himself by the title “the God of Abraham, the God of Isaac, and the God of Jacob” (cf. Ex 3:15).

Commentary of Keil & Delitzsch on Exodus 3:6

Jehovah then made Himself known to Moses as the God of his fathers, Abraham, Isaac, and Jacob, reminding him through that name of the promises made to the patriarchs, which He was about to fulfill to their seed, the children of Israel.

Given the above discussion, Jesus’ argument in Mt 22:32b is astonishing in its simplicity. His point is that God would not refer to Himself in such terms, as “the God of Abraham, the God of Isaac, and the God of Jacob,” if those individuals were not still living. While not conclusive on its own, the present tense of εἰμί (Strong’s G1510 meaning I exist, I am) in Mt 22:32 supports this interpretation.