Basic Matrix Operations for 2x2 Matrices

You are required to implement a Matrix class that performs basic operations on 2x2 matrices. The supported operations are:

1. Addition: Given two 2x2 matrices (A = \begin{pmatrix} a_{11} & a_{12}\ a_{21} & a_{22} \end{pmatrix}) and (B = \begin{pmatrix} b_{11} & b_{12}\ b_{21} & b_{22} \end{pmatrix}), compute ( A+B = \begin{pmatrix} a_{11}+b_{11} & a_{12}+b_{12}\ a_{21}+b_{21} & a_{22}+b_{22} \end{pmatrix}).

2. Subtraction: Compute (A-B) in a similar manner.

3. Multiplication: There are two cases:

   • When multiplying two matrices, perform standard matrix multiplication: ( (A \times B){ij} = \sum{k=1}^{2} a_{ik} \times b_{kj}).
   • When multiplying a matrix by a scalar (k): Multiply each element by (k).

4. Transpose: Compute the transpose (A^T) such that the element at row (i) and column (j) becomes the element at row (j) and column (i).

5. Determinant: For a 2x2 matrix (A = \begin{pmatrix} a & b\ c & d \end{pmatrix}), compute (\det(A) = ad - bc).

6. Equality: Check if two matrices are identical element-wise.

7. String Representation: Return the string representation in a Python list style, e.g. "[[1, 2], [3, 4]]".

Input/Output Requirement: All input is via standard input (stdin) and all output via standard output (stdout).

Input Format: The first line contains an integer (T) representing the number of operations to perform. Then for each operation, the first line is a string indicating the operation type. The supported operation types are: add, sub, mul, smul, trans, det, eq, and str.

For operations add, sub, mul, and eq, the next 4 lines provide two matrices. Each matrix is given by two lines containing two space-separated integers.

For operations trans, det, and str, the next 2 lines describe a single matrix.

For operation smul (scalar multiplication), the next 2 lines describe a matrix, followed by one line containing the scalar.

Output Format: For each operation, output its result as follows:

• For matrix operations (add, sub, mul, smul, trans, str): print the 2x2 matrix in two lines (each line with two space-separated integers or exactly as the string representation for str).
• For det: print a single integer.
• For eq: print either True or False.

Make sure your solution passes all test cases.

inputFormat

The first line contains an integer (T) representing the number of operations. Then, for each operation:

• The first line is a string denoting the operation type (one of: add, sub, mul, smul, trans, det, eq, str).

• For operations requiring two matrices (add, sub, mul, eq):

• The next two lines contain the first matrix (each line with 2 integers).
• The following two lines contain the second matrix (each line with 2 integers).

• For operations requiring one matrix (det, trans, str):

• The next two lines contain the matrix.

• For scalar multiplication (smul):

• The next two lines contain the matrix, followed by one line with a scalar integer.

outputFormat

For each operation, output the result as follows:

• For matrix results (add, sub, mul, smul, trans, str):

• If the operation is not str, print the matrix in 2 lines with each row's entries separated by a space.
• For str, output the string representation, e.g. "[[1, 2], [3, 4]]".

• For det: output a single integer representing the determinant.

• For eq: output either "True" or "False".## sample

2
add
1 2
3 4
4 3
2 1
smul
1 2
3 4
2

5 5
5 5
2 4
6 8

</p>