To determine the identity element of the group of invertible 2x2 matrices with matrix multiplication, we need to find the matrix that, when multiplied with any other matrix in the group, gives back the same matrix.

Let's denote the identity matrix as I. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. In the case of a 2x2 matrix, the identity matrix is:

I = [1 0]
[0 1]

Now, we need to check if the identity matrix satisfies the condition of being the identity element.

Let's take an arbitrary invertible 2x2 matrix A and multiply it with the identity matrix:

A * I = [a b] * [1 0] = [a*1 + b*0 a*0 + b*1] = [a b]
[c d] [0 1] [c*1 + d*0 c*0 + d*1] [c d]

As we can see, the result of multiplying any invertible 2x2 matrix A with the identity matrix I is the matrix A itself. Therefore, the identity element of the group of invertible 2x2 matrices with matrix multiplication is the identity matrix, which is option b.

Question

To determine the identity element of the group of invertible 2x2 matrices with matrix multiplication, we need to find the matrix that, when multiplied with any other matrix in the group, gives back the same matrix.

Let's denote the identity matrix as I. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. In the case of a 2x2 matrix, the identity matrix is:

I = [1 0]
    [0 1]

Now, we need to check if the identity matrix satisfies the condition of being the identity element.

Let's take an arbitrary invertible 2x2 matrix A and multiply it with the identity matrix:

A * I = [a b] * [1 0] = [a*1 + b*0  a*0 + b*1] = [a b]
            [c d]   [0 1]   [c*1 + d*0  c*0 + d*1]   [c d]

As we can see, the result of multiplying any invertible 2x2 matrix A with the identity matrix I is the matrix A itself. Therefore, the identity element of the group of invertible 2x2 matrices with matrix multiplication is the identity matrix, which is option b.

Knowee AI · Accepted Answer

To determine the identity element of the group of invertible 2x2 matrices with matrix multiplication, we need to find the matrix that, when multiplied with any other matrix in the group, gives back the same matrix.

Let's denote the identity matrix as I. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. In the case of a 2x2 matrix, the identity matrix is:

I = [1 0]
    [0 1]

Now, we need to check if the identity matrix satisfies the condition of being the identity element.

Let's take an arbitrary invertible 2x2 matrix A and multiply it with the identity matrix:

A * I = [a b] * [1 0] = [a*1 + b*0  a*0 + b*1] = [a b]
            [c d]   [0 1]   [c*1 + d*0  c*0 + d*1]   [c d]

As we can see, the result of multiplying any invertible 2x2 matrix A with the identity matrix I is the matrix A itself. Therefore, the identity element of the group of invertible 2x2 matrices with matrix multiplication is the identity matrix, which is option b.

The group of invertible 2x2 matrices with matrix multiplication has the identity element:a.The zero matrixb.The identity matrixc.The inverse matrixd.The diagonal matrix

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