diff --git a/gallery/example3.pdf b/gallery/example3.pdf
index ab2412c..2919817 100644
Binary files a/gallery/example3.pdf and b/gallery/example3.pdf differ
diff --git a/gallery/example3.typ b/gallery/example3.typ
index af5e7b3..3b0d861 100644
--- a/gallery/example3.typ
+++ b/gallery/example3.typ
@@ -25,3 +25,16 @@ $
 $
   E = #mat.display(E)
 $
+
+#let M = mat.mat(
+  (2, 4, 5, 6),
+  (-1, 5, 6, 9),
+  (3, 7, 1, -6),
+  (4, -2, 3, 5)
+)
+$M = #mat.display(M)$
+
+#let d = mat.det(M)
+$det(M) = #d$
+
+#mat.det-steps(M)
\ No newline at end of file
diff --git a/src/mat.typ b/src/mat.typ
index 8fefc3d..0954883 100644
--- a/src/mat.typ
+++ b/src/mat.typ
@@ -43,9 +43,9 @@
   return mat(..rows)
 }
 
-#let display(mat) = {
+#let display(mat, ..args) = {
   _check(mat)
-  math.mat(..mat.rows)
+  math.mat(..mat.rows, ..args.named())
 }
 
 #let add(mat1, mat2) = {
@@ -184,4 +184,102 @@
   }
 
   return mat2
+}
+
+#let co-mat(mat1, elim-x, elim-y) = {
+  _check(mat1)
+  let mat2 = of-size(mat1.h - 1, mat1.w - 1)
+  for y in range(mat2.h) {
+    for x in range(mat2.w) {
+      let ox = if x < elim-x {x} else {x + 1}
+      let oy = if y < elim-y {y} else {y + 1}
+      mat2.rows.at(y).at(x) = mat1.rows.at(oy).at(ox)
+    }
+  }
+  return mat2
+}
+
+#let det(mat) = {
+  _check(mat)
+  if mat.w != mat.h {
+    panic("Matrix must be square")
+  }
+
+  if mat.w == 0 {
+    return 1
+  }
+
+  let res = 0
+  for y in range(mat.h) {
+    let sign = (1 - 2 * calc.rem(y, 2))
+    let co-fact = det(co-mat(mat, 0, y))
+    res += sign * mat.rows.at(y).at(0) * co-fact
+  }
+  return res
+}
+
+#let det-steps(mat) = {
+  _check(mat)
+  if mat.w != mat.h {
+    panic("Matrix must be square")
+  }
+
+  let res = []
+  let lines = ()
+  res += display(mat, delim: "|")
+  let ap = $&$.body
+
+  let terms = ((1, mat,),)
+  for _ in range(mat.w - 2) {
+    let line = [
+      #ap =
+    ]
+    
+    for (i, term) in terms.enumerate() {
+      let (coef, m) = term
+
+      let sub-terms = ()
+      for y in range(m.h) {
+        let c = (1 - 2 * calc.rem(y, 2)) * coef * m.rows.at(y).at(0)
+        let m2 = co-mat(m, 0, y)
+        if c != 0 {
+          sub-terms.push((c, m2))
+        }
+
+        if y + i != 0 and c >= 0 {
+          line += [+]
+        }
+        if c != 1 {
+          if c == -1 {
+            line += [-]
+          } else {
+            line += [#c #sym.dot]
+          }
+        }
+        line += display(m2, delim: "|")
+      }
+
+      terms.at(i) = sub-terms
+    }
+    lines.push(line + linebreak())
+    terms = terms.join()
+  }
+
+  res += lines.join()
+
+  res += [#ap =]
+  let total = 0
+  for (i, term) in terms.enumerate() {
+    let (coef, m) = term
+    let value = coef * det(m)
+    total += value
+    if value != 0 {
+      if i != 0 and value >= 0 {
+        res += [+]
+      }
+      res += [#value]
+    }
+  }
+  res += [=#total]
+  return math.equation(res)
 }
\ No newline at end of file