diff --git a/basic-geometry/matrix3x3.h b/basic-geometry/matrix3x3.h
index b0bd7c6..b8554b0 100644
--- a/basic-geometry/matrix3x3.h
+++ b/basic-geometry/matrix3x3.h
@@ -280,6 +280,22 @@ inline int bgc_matrix3x3_is_rotation_fp32(const BgcMatrix3x3FP32* matrix)
         return 0;
     }
 
+    BgcMatrix3x3FP32 transposed, product;
+
+    bgc_matrix3x3_transpose_fp32(matrix, &transposed);
+    bgc_matrix_product_3x3_at_3x3_fp32(matrix, &transposed, &product);
+
+    return bgc_is_unit_fp32(product.r1c1) && bgc_is_zero_fp32(product.r1c2) && bgc_is_zero_fp32(product.r1c3)
+        && bgc_is_zero_fp32(product.r2c1) && bgc_is_unit_fp32(product.r2c2) && bgc_is_zero_fp32(product.r2c3)
+        && bgc_is_zero_fp32(product.r3c1) && bgc_is_zero_fp32(product.r3c2) && bgc_is_unit_fp32(product.r3c3);
+}
+
+inline int bgc_matrix3x3_is_rotation_fp32a(const BgcMatrix3x3FP32* matrix)
+{
+    if (!bgc_is_unit_fp32(bgc_matrix3x3_get_determinant_fp32(matrix))) {
+        return 0;
+    }
+
     const float product_r1c1 = matrix->r1c1 * matrix->r1c1 + matrix->r1c2 * matrix->r2c1 + matrix->r1c3 * matrix->r3c1;
     const float product_r1c2 = matrix->r1c1 * matrix->r1c2 + matrix->r1c2 * matrix->r2c2 + matrix->r1c3 * matrix->r3c2;
     const float product_r1c3 = matrix->r1c1 * matrix->r1c3 + matrix->r1c2 * matrix->r2c3 + matrix->r1c3 * matrix->r3c3;
diff --git a/basic-geometry/slerp.c b/basic-geometry/slerp.c
index 43f5cf0..40753eb 100644
--- a/basic-geometry/slerp.c
+++ b/basic-geometry/slerp.c
@@ -40,17 +40,17 @@ void bgc_slerp_make_fp32(const BgcVersorFP32* start, const BgcVersorFP32* augmen
 
     slerp->radians = atan2f(vector_modulus, augment->s0);
 
-    const float mutliplier = 1.0f / vector_modulus;
+    const float multiplier = 1.0f / vector_modulus;
 
     slerp->s0_cos_weight = start->s0;
     slerp->x1_cos_weight = start->x1;
     slerp->x2_cos_weight = start->x2;
     slerp->x3_cos_weight = start->x3;
 
-    slerp->s0_sin_weight = -mutliplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
-    slerp->x1_sin_weight = mutliplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
-    slerp->x2_sin_weight = mutliplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
-    slerp->x3_sin_weight = mutliplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
+    slerp->s0_sin_weight = -multiplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
+    slerp->x1_sin_weight = multiplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
+    slerp->x2_sin_weight = multiplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
+    slerp->x3_sin_weight = multiplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
 }
 
 void bgc_slerp_make_fp64(const BgcVersorFP64* start, const BgcVersorFP64* augment, BgcSlerpFP64* slerp)
@@ -81,15 +81,15 @@ void bgc_slerp_make_fp64(const BgcVersorFP64* start, const BgcVersorFP64* augmen
 
     slerp->radians = atan2(vector_modulus, augment->s0);
 
-    const double mutliplier = 1.0 / vector_modulus;
+    const double multiplier = 1.0 / vector_modulus;
 
     slerp->s0_cos_weight = start->s0;
     slerp->x1_cos_weight = start->x1;
     slerp->x2_cos_weight = start->x2;
     slerp->x3_cos_weight = start->x3;
 
-    slerp->s0_sin_weight = -mutliplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
-    slerp->x1_sin_weight = mutliplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
-    slerp->x2_sin_weight = mutliplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
-    slerp->x3_sin_weight = mutliplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
+    slerp->s0_sin_weight = -multiplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
+    slerp->x1_sin_weight = multiplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
+    slerp->x2_sin_weight = multiplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
+    slerp->x3_sin_weight = multiplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
 }