Find the inverse of the matrix A = [2 5; 1 3].a.[3 1; -5 2]b.[3 -5; -1 2]c.[2 -5; 1 3]d.[3 -1; -5 2]

Question

a.[3 1; -5 2] b.[3 -5; -1 2] c.[2 -5; 1 3] d.[3 -1; -5 2]

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To find the inverse of a 2x2 matrix A = [a b; c d], we use the formula:

A^(-1) = 1/(ad-bc) * [d -b; -c a]

Given the matrix A = [2 5; 1 3], we can substitute into the formula:

A^(-1) = 1/(23 - 51) * [3 -5; -1 2]

This simplifies to:

A^(-1) = 1/1 * [3 -5; -1 2]

So, the inverse of the matrix A is [3 -5; -1 2], which corresponds to option b.

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