Working with backpropagation algorithm using softmax function in the neural network
You are almost there. However, you need to transpose dA, e.g. with numpy.transpose(dA).
Then you will have the right dimensions of dA and dZ to perform matrix multiplication.
I am creating a Neural Network from scratch for MNIST data, so I have 10 classes in the output layer. I need to perform backpropagation and for that, I need to calculate dA*dZ for the last layer where dA is the derivative of the loss function L wrt the softmax activation function A and dZ is the derivative of the softmax activation functionA wrt to z where z=wx+b. The size obtained for dA is 10*1 whereas the size obtained for dZ is 10*10. 
Is it correct? If yes, who do I multiply dA*dZ as they have different dimension.