If A is a square matrix, then which of the following is correct ? (a) AAT is symmetric matrix and ATA is skew-symmetric matrix. (b) AAT is skew-symmetric matrix and ATA is symmetric matrix. (c) Both AAT and ATA are symmetric matrices. (d) Both AAT and ATA are skew-symmetric matrices.

If A is a square matrix, then which of the following is correct ? (a)

1.	If A is a square matrix, then which of the following is correct ? (a) AAT is symmetric matrix and ATA is skew-symmetric matrix. (b) AAT is skew-symmetric matrix and ATA is symmetric matrix. (c) Both AAT and ATA are symmetric matrices. (d) Both AAT and ATA are skew-symmetric matrices.
Answer» If $A$ is a square matrix, then which of the following is correct ? $(a)$ $A A^{T}$ is symmetric matrix and $A^{T} A$ is skew-symmetric matrix. $(b)$ $A A^{T}$ is skew-symmetric matrix and $A^{T} A$ is symmetric matrix. $(c)$ Both $A A^{T}$ and $A^{T} A$ are symmetric matrices. $(d)$ Both $A A^{T}$ and $A^{T} A$ are skew-symmetric matrices.