Question

Multiplication of two 2X2 matrices is ___.

A-open
B-not possible
C-closed

Answer 1

• C-closed

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The multiplication of two 2x2 matrices is closed.

Matrix multiplication is an operation that combines two matrices to create a new matrix.

When multiplying two 2x2 matrices, we follow a specific rule that ensures the resulting matrix is also a 2x2 matrix.

The result is a new 2x2 matrix, which means the multiplication of two 2x2 matrices is closed.

For example, let's say we have A and B:

• 
  `A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]`

• 
  `B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]`

The resulting matrix, let's call it Matrix C, will be:

`C=\left[\begin{array}{cc}ae + bg&a.f + bh\\ce + dg&cf + dh\end{array}\right]`

As we see, Matrix C is also a 2x2 matrix, satisfying the definition of a closed operation.

Therefore, the correct answer is C.