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 = 3, A₁₂ = -4, A₂₁ = 2, A₂₂ = 2.

∴ Adj A =

=

And |A| = 2(3)-(-2)(4) = 14

So .