Given a square matrix A, the characteristic polynomial of A is defined as
Pₐ(t) det(tI - A),

where I is the identity matrix. For example, if A = ( 1 2 ) , then the characteristic polynomial o of A is
( 3 4 )

PA(t) = det (I-A) = det (t( 1 0 ) - ( 1 2 ) )
( 0 1 ) ( 3 4 ) )

and rewriting the difference as a single matrix, this becomes

det ( t - 1 -2 ) =(t-1)(-4) -(-2)(-3) = t²-5t-2.
( -3 t - 4 )

Compute the characteristic polynomial of the matrix

A = ( a b )
( c d )

Express your answer in the form p₂t² + P₁t + Po.