Video Transcript
Find the determinant of the two-by-two matrix five, zero, zero, five.
In this question, we’re given a two-by-two matrix, and we’re asked to find the determinant of this matrix. So, the first thing we’re going to need to do is recall what we mean by the determinant of a matrix. First, recall we can use this vertical bar notation to represent the determinant of a matrix. Next, we need to recall how we actually calculate the determinant of this matrix.
To do this, we need to recall the determinant of a two-by-two matrix is the difference between the products of its diagonals. So, this gives us the determinant of the two-by-two matrix 𝑎𝑑 minus 𝑏𝑐 is equal to the product of the first diagonal, 𝑎 times 𝑑, minus the product of the second diagonal, 𝑏𝑐.
We can use this to find the determinant of the matrix given to us in the question. We need to calculate the determinant of the two-by-two matrix five, zero, zero, five. First, we need to calculate the product of five multiplied by five. Then, we need to subtract the product of zero multiplied by zero. So, the determinant of this matrix is five multiplied by five minus zero multiplied by zero. And we can calculate this. It’s just equal to 25. And this gives us our final answer of 25.
And it’s also worth pointing out we could have thought about this as a formula for finding the two-by-two determinant, where we substitute 𝑎 is equal to five, 𝑑 is equal to five, and 𝑏 and 𝑐 are both equal to zero. This would also give us the correct answer of 25. Therefore, we were able to show the determinant of the two-by-two matrix five, zero, zero, five is equal to 25.