While multiplying A with A itself, we are getting a number whose ones digit is A again.

But, This happens only when A = 1, 5, or 6

Now,

If A = 1, then the multiplication will be 11 × 1 = 11. But, here the tens digit is given as 9

Therefore, A = 1 is invalid.

Similarly,

If A = 5, then the multiplication will be 15 × 5 = 75. Thus, A = 5 is also invalid.

If we take A = 6, then 16 × 6 = 96

Therefore, A should be 6

The multiplication is as follows:

Hence, the value of A is 6