# Evaluate the determinant of each of the following matrices: a. [[5,6],[7,3]] b. [[2,4],[-3,-5]]

Evaluate the determinant of each of the following matrices:
a. $\left[\left[5,6\right],\left[7,3\right]\right]$
b. $\left[\left[2,4\right],\left[-3,-5\right]\right]$
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doplovif
a) To calculate the determinant according to the formula,
$det\left[\left[a,b\right],\left[c,d\right]\right]=ad-bc$
So, $\left[\left[5,6\right],\left[7,3\right]\right]=5\ast 3-6\ast 7$
=15-42
=-27
Hence the determinant of the matrices is -27
b) To calculate the determinant,
$\left[\left[2,4\right],\left[-3,-5\right]\right]=2\ast \left(-5\right)-4\left(\ast -3\right)$
=-10+12
=2
Hence the determinant of the given matrices is 2