The Que Below AB and P are any n by n matrices Are the foll

The Que. : Below A,B and P are any n by n matrices. Are the following formulas True of False? Prove the statements g and h if it is true. Give a counterexample for the statements g and h if it is false.

Solution

G.

True,

A*A^T = 1

take determinant of both sides,

det A * det A^T = det 1

We know that

det 1 = 1

det A^T = det A

(det A)^2 = 1

det A = sqrt 1

det A = +1 or -1

H.

False

A = [1 2],[1 3]

det A = 1

A^T = [1 1],[2 3]

A*A^T = [5 7],[7 10]

A*A^T is not equals to I