Q21 of 124 Page 213

If the matrix A is both symmetric and skew-symmetric, show that A is a zero matrix.

Given that matrix A is both symmetric and skew symmetric, then,

We have A = A’ ……(i)

And A = -A’ ……(ii)

From (i) and (ii) we get,

A’ = -A’,

2A’ = 0

A’ = 0

Then, A = 0

Hence proved.

If and find a matrix X such that

3 A – 2B + X = O.

If show that A’ A = I.

If A and B are symmetric matrices of the same order, show that (AB – BA) is a skew symmetric matrix.

If and f(x) = x² – 4x + 1, find f(A).