Mathematics 2003 JAMB Past Questions - Question 21: A matrix p has an inverse P¯¹ = (1 -3 (0 1) find P

Correct Answer

D

Explanation

To find the matrix P, we can use the formula for the inverse of a 2x2 matrix:P⁻¹ = (1/det(P)) * adj(P)Where det(P) is the determinant of matrix P and adj(P) is the adjugate of matrix P.From the given information, we have:P⁻¹ = (1 -3 (0 1)To find the determinant of P, we can use the formula:det(P) = 1 * 1 - (-3 * 0) = 1Now, let's find the adjugate of P:adj(P) = (1 -3 (0 1)Since det(P) = 1, we can substitute the values into the formula for the inverse:P⁻¹ = (1/det(P)) * adj(P)P⁻¹ = (1/1) * (1 -3 (0 1)P⁻¹ = 1 * (1 -3 (0 1)P⁻¹ = (1 -3 (0 1)Therefore, the matrix P is (1 -3 (0 1).