4. Let A be a square matrix with transpose A". • If AT = A, then A is called a symmetric matrix. %3D • If AT = -A, then A is called a skew-symmetric matrix. (a) Write down an example of a nonsingular 4 × 4 symmetric matrix. (b) Write down an example of a nonsingular 4 x 4 skew-symmetric matrix. ) Use properties of the transpose to show that if B is any m × n matrix, then (c) the matrix A = BT B is symmetric. 'In general, if A is an orthogonal matrix with det(A) = 1, then A is called a special orthogonal matrix. (d) matrix, then In + A+ 2A² + 3A³ is also symmetric. Use properties of the transpose to show that if A is any n × n symmetric

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