# If A is a square matrix then AA’ + A’A is a a) unit matrix b) null matrix c) symmetric matrix d) skew symmetric matrix

Saurabh Koranglekar
4 years ago
Vikas TU
14149 Points
4 years ago

• Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other.

• An m x n matrix A is said to be a square matrix if m = n i.e. number of rows = number of columns.

• In a square matrix the diagonal from left hand side upper corner to right hand side lower corner is known as leading diagonal or principal diagonal.

• The sum of the elements of a square matrix A lying along the principal diagonal is called the trace of A i.e. tr(A). Thus if A = [aij]n×n, then tr(A) = ∑ni=1  aii = a11 + a22 +......+ ann.

• For a square matrix A = [aij]n×n, if all the elements other than in the leading diagonal are zero i.e. aij = 0, whenever i ≠ j then A is said to be a diagonal matrix.

• A matrix A = [aij]n×n is said to be a scalar matrix if aij = 0, i ≠ j

= m, i = j, where m ≠ 0

Akash
13 Points
3 years ago
Here we use the property of transpose of matrix
(AA’ + A’A)’ = (AA’)’ + (A’A)’
= AA’ + A’A
Therefore, (AA’+A’A)’ = AA’ + A’A
Hence the given is symmetric matrix