Finding the determinant of a 2x2 matrix

As a hint, I'll take the determinant of a very similar two by two matrix.

So we wanna figure out the determinant of this matrix and we can denote it

by the determinant of the 2x2 matrix five,

three,negative one and four

and the definition of determinant of the 2x2 matrix like this, as we can first take

this diagonal, five times four

so write it down, just going to be equal to

5 * 4 minus of product of that diagonal

...so what is this

give us? So, five times four is twenty

and then three times negative one will be negative three

this is negative three...

but making negative the negative three will make the positive three

so the determinant of this matrix is twenty three.