$1.$ Enter each of the matrices A$,$ B$,$ and C as Numpy matrix. $2.$ What are the dimensions of each of the matrices A$,$ B$,$ and C$?$ Display these using Python code. $3.$ Determine if each of the following matrix operations is defined. If it is defined, calculate the result using Python. If it is not defined, explain why it is not defined. $($a$)$ A $+$ B $($b$)$ AB $($c$)$ AC $($d$)$ C T $4.$ Illustrate the following property of matrix transpositions using these matrices: $($A $+$ B$)$ T $=$ AT $+$ BT $.5.$ Illustrate the following property of matrix transposition using these matrices $($AC$)$ T $=$ C T AT $.6.$ Fine C $1$ using Python code.