$a)$

$1^2=1\cdot 1=1$

$2^2=2\cdot 2=4$

$3^2=3\cdot 3=9$

$4^2=4\cdot 4=16$

$5^2=5\cdot 5=25$

$b)$

$6^2=6\cdot 6=36$

$7^2=7\cdot 7=49$

$8^2=8\cdot 8=64$

$9^2=9\cdot 9=81$

${10}^2=10\cdot 10=100$