The following statements are true for matrices:

1. (AB)-1 = B-1A-1: This is known as the inverse of a product of matrices. The inverse of the product of two matrices A and B is the product of the inverse of B and the inverse of A, in that order.

2. (AT) = A: This is not generally true. AT denotes the transpose of matrix A. The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. It is only true if A is a symmetric matrix, meaning A = AT.

3. AB = BA: This is not generally true. Matrix multiplication is not commutative, meaning that the order in which matrices are multiplied can affect the result.

4. A*I = I: This is not true. When a matrix A is multiplied by the identity matrix I, the result is the original matrix A, not I.

So, the only universally true statement for matrices in the given options is (AB)-1 = B-1A-1.

Question

The following statements are true for matrices:

1. (AB)-1 = B-1A-1: This is known as the inverse of a product of matrices. The inverse of the product of two matrices A and B is the product of the inverse of B and the inverse of A, in that order.

2. (AT) = A: This is not generally true. AT denotes the transpose of matrix A. The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. It is only true if A is a symmetric matrix, meaning A = AT.

3. AB = BA: This is not generally true. Matrix multiplication is not commutative, meaning that the order in which matrices are multiplied can affect the result.

4. A*I = I: This is not true. When a matrix A is multiplied by the identity matrix I, the result is the original matrix A, not I.

So, the only universally true statement for matrices in the given options is (AB)-1 = B-1A-1.

Knowee AI · Accepted Answer

The following statements are true for matrices:

1. (AB)-1 = B-1A-1: This is known as the inverse of a product of matrices. The inverse of the product of two matrices A and B is the product of the inverse of B and the inverse of A, in that order.

2. (AT) = A: This is not generally true. AT denotes the transpose of matrix A. The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. It is only true if A is a symmetric matrix, meaning A = AT.

3. AB = BA: This is not generally true. Matrix multiplication is not commutative, meaning that the order in which matrices are multiplied can affect the result.

4. A*I = I: This is not true. When a matrix A is multiplied by the identity matrix I, the result is the original matrix A, not I.

So, the only universally true statement for matrices in the given options is (AB)-1 = B-1A-1.

Which of the following is true for matrices?Review Later(AB)-1 = B-1A-1(AT) = AAB = BAA*I = I

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