Question

Let A be the 2 x 2 matrices given by A = [aij], where a; € {0,1,2,3,4} such that a11 + a12 +a21 + a22 = 4 . Find the number of matrices A such that A is invertible.​

Answer 1

$\mathfrak{Answer}$

Given tr(A)=4

⇒a11 +a22 =4

a ii ={0,1,2,3,4}

So, diagonal entries of A can be 0 and 4 , 4 and 0, 1 and 3, 3 and 1, 2 and 2,

Hence, 5 matrices are possible