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One (1) is not the same as Eleven (11). 11 is not 1 and 1, it's Ten more than One.

If you have 11 people, and want to give them each 11 apples, you'll need 121 apples.

11 x 11 means 11 groups of 11, just like 10 x 10 means ten groups of ten. Ten groups of ten gives you 100 total objects, 11 groups of 11 gives you 121 of whatever you’re counting. You can try it with squares of grid paper if you don’t believe me.

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11x11 is asking how many total if we have 11 groups each with 11 per group? One group of 11 is 11, 2 groups is 22, 3 groups are 33, 4 groups are 44..... And 11 groups are 121

There are some lapses in thinking multiplying is all just 1x1.

Let’s think of it differently by thinking of apples.

When we add, we are counting how many apples in total we have. Let’s say we count all the apples in a tree, and we have 25. Then on another tree, there are another 25. We add those (25+25) and we get a total of 50 apples.

When we multiply, we’re considering units or groups of things. If I have a bag of apples, and each bag hold 5 apples, then I have 5 apples total. If I have multiple bags (let’s say 8 bags) then I’m going to multiply.

Since each bag holds 5 apples, and I have 8 total bags, I’ll multiply 5 apples (per bag) by 8 bags which leaves me with 40 apples.

In your question, we would have 11 groups of 11, which ends with 121; you would use 11+11 if you were adding 2 groups of 11.