12. (5 points) The last two digits of the product of 1991 multiplied by itself 1991 times are

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【Answer】1 1991's last two digits are 91;
2 1991s multiplied together have a product with the last two digits being 81;
3 1991s multiplied together have a product with the last two digits being 71;
4 to 10 1991s multiplied together have products with the last two digits being 61;
and so on: the last two digits of the products of 5 to 10 1991s are $51, 41, 31, 21, 11, 01$;
and the last two digits of the product of 11 1991s are 91.
From this, we can see that the last two digits of the product of every 10 1991s repeat, i.e., the cycle is 10.
$1991 \div 10=199$ remainder $\cdots 1$, so it should be 91.