If A is a square matrix, then AA' is a (A' is the transpose of the matrix A)

Question

If A is a square matrix, then AA' is a (A' is the transpose of the matrix A) (A) unit matrix (B) null matrix (C) symmetric matrix (D) skew-symmetric matrix

Tardigrade Admin · Accepted Answer

Now, (AA')'=(A')'A'=AA' ∴ AA' is asymmetric matrix.

Q. If A is a square matrix, then AA' is a (A' is the transpose of the matrix A)

unit matrix

null matrix

symmetric matrix

skew-symmetric matrix

Now, $(A A^{'})^{'} = (A^{'})^{'} A^{'} = A A^{'}$
$∴$ $A A^{'}$ is asymmetric matrix.

Q. If A is a square matrix, then AA' is a (A' is the transpose of the matrix A)

unit matrix

null matrix

symmetric matrix

skew-symmetric matrix

Now, (AA′)′=(A′)′A′=AA′ ∴ AA′ is asymmetric matrix.

Now, $(A A^{'})^{'} = (A^{'})^{'} A^{'} = A A^{'}$
$∴$ $A A^{'}$ is asymmetric matrix.