Question:
Show that A¢A and AA¢ are both symmetric matrices for any matrix A.
Solution:
Let P = A¢A
So, P¢ = (A¢A) ¢
= A¢(A¢)¢ [As (AB) ¢ = B¢A¢]
Hence, A¢A is symmetric matrix for any matrix A.
Now, let Q = AA¢
So, Q¢ = (AA¢)¢ = (A) ¢ = AA¢ = Q
Hence, AA¢ is symmetric matrix for any matrix A.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.