# Class 12 RD Sharma Solutions- Chapter 5 Algebra of Matrices – Exercise 5.5

### Question 1: Solution:

Given: Consider, From equation (1) and (2) it can be seen that,

A skew-symmetric matrix is a square matrix whose transpose equal to its negative, that is,

X = −XT

So, A − AT is a skew-symmetric.

### Question 2: Solution:

Given: Consider, From equation (1) and (2) it can be seen,

A skew-symmetric matrix is a square matrix whose transpose equals its negative, that is,

X = −XT

Thus, A − AT is a skew-symmetric matrix.

### Question 3: Solution:

Given: As we know that A = [aij]m×n is a symmetric matrix if aij = aji

Thus,

x = a13 = a31 = 4

y = a21 = a12 = 2

z = a22 = a22 = z

t = a32 = a23 = −3

Hence, x = 4, y = 2, t = −3 and z can have any value.

### Question 4: Solution:

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