Find the inverse of each of the matrices (if it exists)

Question

Philoid · Accepted Answer

We know that

Adjoint of the matrix A = [a_ij]_n×n is defined as the transpose of the matrix [A_ij]_n×n where A_ij is the co-factor of the element a_ij.

Let’s find the cofactors for all the positions first-

Here, A₁₁ = 2, A₁₂ = 3, A₂₁ = -5, A₂₂ = -1.

∴ Adj A =

=

And |A| = -1(2)-(-3)(5) = 13

So